Rainbow-colored brioche bun

Ingredients:

• 2 and 3/4 cups premium flour
• 1 and 1/4 teaspoons active dry yeast (about half a 7g packet)
• 2 tablespoons of sugar
• 2.5 tsp coarse salt
• 0.5 cups whole milk
• 4 large eggs
• 140g unsalted butter, diced, at room temperature, plus extra for greasing
• Red, orange, yellow, green, blue and purple gel food coloring
• Special equipment: 1 x 22 x 12 cm non-stick bread pan

Preparation:

1. In the bowl of a stand mixer, combine the flour, yeast, sugar, and salt and mix with the dough hook attachment on low speed until evenly combined. Add the milk and 3 eggs and mix on low speed until smooth. Increase the mixer speed to medium-high and mix until the dough begins to pull away from the sides of the bowl, about 5 minutes.
2. Reduce the speed to medium and begin adding the butter a few pieces at a time, waiting until fully incorporated before adding more, about 5 minutes. Increase the speed to medium-high and continue mixing until the dough is glossy and slightly sticky, about 7 minutes.
3. Divide the dough into 6 equal-sized pieces. Add a few drops of red food coloring to one piece of dough and stir until no bright stripes remain; set aside. Repeat with the remaining 5 pieces of dough, tinting each one with one of the remaining colors (orange, yellow, green, blue, or purple).
4. Place each colored piece of dough in a separate small bowl and cover with plastic wrap. Refrigerate for at least 8 hours and up to 12 hours.
5. To assemble, roll out six pieces of chilled dough individually on a sheet of parchment paper into six 22 x 12 cm rectangles. Stack the layers in rainbow color order (red on the bottom, then orange, yellow, green, blue, and purple). Roll out the dough again into a 30 x 20 cm rectangle; this will ensure all the layers stick together and bake evenly. Place the stack red-side down and, starting from the shorter end, roll the dough into a tight log.
6. Generously grease a 9 x 5-inch (22 x 12 cm) nonstick loaf pan and place the loaf seam-side down inside. Generously grease a piece of plastic wrap large enough to cover the entire pan and place it, buttered side down, loosely over the pan. Let the dough rise until it extends 1/2 inch (1 cm) over the edges of the pan, 2-3 hours.
7. Position a rack in the middle of the oven and preheat the oven to 175°C.
   
   
   When measuring flour, spoon it into a dry measuring cup and remove any excess. Scooping flour directly from the bag with a measuring cup will compact it, resulting in dry baked goods.
8. Beat the remaining 1 egg with 1 tablespoon of water. Remove the plastic wrap and brush the top of the dough with the beaten egg. Bake until golden brown and a thermometer inserted into the center registers 185°F (88°C), about 30 minutes, rotating the pan halfway through baking.
9. Transfer the bread to a wire rack and let cool for 5 minutes, then run a knife around the edges to loosen the bread from the pan and turn it out onto the rack. Let cool completely on the rack.