I believe that humility is necessary if you want to be successful in the kitchen and life in general. It would be pretty hard to go through life not taking others advice, always assuming you're right, and never backing down from an argument. I try and practice humility as much as possible when I make something new, or when I don't think I have something down perfectly. Using or listening to someone else's view can save you a lot of time and frustration. This is not one of those times though. I'm not saying this recipe is perfect, and I am not saying it is the best. What I am saying is that this recipe far exceeded my expectations, and I can pretty much guarantee it will do so for you as well.
Before I go any further I have to nod my head to Smitten Kitchen for the skeleton of this recipe. I would never pull a recipe like this out of thin air, so I think it is important to give credit where it is due. That said, SK's recipe was for a light brioche bun, so I messed with that recipe and opted for a heavier brioche bun by doubling the amount of eggs and using heavy cream in place of milk then I applied my typical technique for yeast breads to the dough as well.
The most important thing you can do to make any good bread (or buns in this case) is proofing your yeast. For one reason or another I find that store bought yeast can be hit or miss, and you should never assume it is healthy. To test and see if it is healthy and ready to make a good bread for you, all we do is simply reconstitute it into some water with a little sugar and see if it foams after a little time passes. If your yeast doesn't foam, pour it out and start with new water, cream, sugar, and yeast. If you skip this step and your yeast is bad you will not get desirable results. I can promise you that.
I know it might be asking a lot, but please try and follow the temperatures, ingredients, and instructions as well as possible. Like I said before this recipe isn't perfect, but there is a reason for each stipulation that I make here.
5 tablespoons heavy cream
1 cup water
2 1/4 teaspoons dry yeast
2 1/2 tablespoons sugar
3 extra large eggs, room temperature
4 cups bread flour
1 1/2 teaspoons salt
2 1/2 teaspoons butter, room temperature
Extra virgin olive oil
Sesame seeds (optional)
1. Mix the water, 3 tablespoons of heavy cream, and the sugar in a microwave safe container. Microwave this at 30 second intervals until you get the mixture between 105F to 108F. Sprinkle the yeast on top and let this sit for 7 to 10 minutes, or until foamy. (If it doesn't foam start over from the beginning.)
2. While the yeast proofs, sift the flour into a large bowl. Measure 3 cups of sifted flour from this bowl and add it to another large bowl. Whisk the salt into this bowl to distribute the salt evenly.
3. Slice the butter into thin squares and add this to the flour and salt mixture. Use a fork to mash the butter into the side of the bowl, or lightly mix the butter into the flour with your hands. Set aside.
4. Add two of the eggs into a small bowl and whisk them very well. Set aside.
5. Pour the yeast starter into the flour and lightly mix with a fork until the liquid is evenly distributed. (It should be rather clumpy and dry at this point.)
6. Add the eggs to the dough and mix well with a fork and then with your hands, until a wet sticky dough has formed.
7. Cover your work surface with 1/2 cup of the leftover flour and knead the dough for 5 to 8 minutes, adding more flour during this time as needed. (Do not use more than the 1 cup of flour though, you want this dough to be a bit stickier than your usual yeast dough.)
8. Once the dough is kneaded, lightly oil a large bowl with olive oil and turn the dough over in it to coat. Place a piece of plastic wrap on this to cover the top, and then refrigerate overnight, or at least 8 hours.
9. Once the dough has risen overnight, remove it from the bowl and lightly over it in flour so it does not stick to the table. Gently press down on the dough and form it into a circle.
10. Cut the circle into 4 equal pieces and then cut these pieces in half. (It is helpful to use a scale and weigh them to the same weight here, but it is not necessary.)
11. Cut two pieces of parchment paper to fit a baking sheet. Roll the 8 pieces of dough into evenly shaped balls and press down on them to form a circle. Evenly place 4 circles of dough onto each piece of parchment paper and then spray with some cooking oil. Cover them with plastic wrap and let them rise for two hours.
12. Just before the buns are done rising, preheat an oven to 400F. Place a pan on the bottom rack and set the top rack in the middle of the oven. Pour about two cups of water into the pan and let the oven preheat.
13. While the oven preheats crack the last egg into a small bowl and add the last two tablespoons of heavy cream. Whisk this together and baste the first four dough circles with the egg wash. (Sprinkle the circles with sesame seeds now if you want to.)
14. Bake the buns for eight minutes on a sheet pan for 8 minutes and then rotate 180° and cook for another 8 minutes, or until the tops are light brown and crisp. Remove them from the oven and place them on a cooling rack until ready to serve, or until the come to room temperature.
15. Bake the other 4 buns in the same fashion.