Small brioche buns

Ingredients:

• 1/2 cup warm water (43-49 °C)
• 1 packet (7 g) of dry yeast
• 3 tablespoons of sugar
• 6 very large eggs, room temperature
• 4.5 cups premium flour
• 2.5 tsp coarse salt
• 170 g butter, room temperature
• 1 egg mixed with 1 tbsp milk, for egg wash

Preparation:

1. Combine the water, yeast, and sugar in the bowl of an electric mixer fitted with the paddle attachment. (If the bowl is cold, use warmer water so that the water is at least 110°F (43°C) when you add the yeast.) Mix the mixture by hand. Let it sit for 5 minutes, until the yeast and sugar dissolve.
2. Add the eggs and beat on medium speed for 1 minute, until well combined. Reduce the speed to low, add 2 cups of flour, salt, and mix for 5 minutes. Without changing the speed, add 2.5 cups of flour and mix for another 5 minutes. Scrape down the sides of the dough, then turn it out into a large, greased bowl and cover with plastic wrap. Refrigerate overnight.
3. The next day, let the dough rest at room temperature for 1 hour. Meanwhile, grease 20 mini muffin tins.
4. Place the dough in the bowl of an electric mixer fitted with a dough hook. Add chunks of softened butter. Mix for 2 minutes, or until a ball forms, adding additional flour if necessary.
5. Place the mixture on a lightly floured board and divide into 20 balls (50g each). Divide these into mini-molds, cover with a damp towel, and set aside. Let the dough rise at room temperature until it doubles in size (about 2 hours).
6. Preheat the oven to 180°C (350°F). Once the brioches have risen, brush the tops of each with egg wash. Bake for 20 minutes, or until they leave an indentation when pressed and sound slightly hollow when tapped. Turn the brioches out of the pans onto a wire rack to cool.