In the bowl of a mixer, use the paddle to combine the flour, sugar, and yeast and mix on low speed briefly. Add the salt and mix for about 10 seconds.
4 ⅔ cup (600 grams) bread flour, ¼ cup (100 grams) granulated sugar, 2 ¼ teaspoons instant yeast, 2 teaspoons salt
Add the egg, milk, and the starter. Mix on low speed.
2 large eggs, ¼ cup (60mL) whole milk, roux starter
When the dough starts to come together, switch to the dough hook. (If the dough doesn't come together, add an additional tablespoon of milk at a time).
Add the butter cubes a one at a time, waiting until the butter has been incorporated before adding another.
½ cup (8 tablespoons or 113 grams) unsalted butter, softened and cut into cubes
Increase the speed to medium and knead for 7 to 10 minutes. At the end of kneading, the dough should be soft and tacky but not sticky and it should pull and stretch easily.
Divide the dough in half, and place one half into a greased bowl and cover it with plastic.
Divide the remaining dough into sixths. Because the amount of dough is so small, it is easiest to work the food coloring in by hand (although you may want to wear a glove to prevent the coloring from getting on your hands). Once you've worked all of the color in as evenly as possible, form the dough into a ball. Leave the rainbow colored balls on a tray or plate and cover with plastic wrap to rise until doubled in size, about 60 minutes.
food coloring
Lightly butter a 13" by 4" by 4" Pullman loaf pan, including the lid or two standard loaf pans.
There are multiple ways to shape the rainbow bread. To make a rainbow swirl bread, use a rolling pin to roll out the white dough into a rectangle. Then roll out the rainbow dough, starting with purple. After each addition, use the rolling pin to seal the dough together. After you have added the red, roll up the loaf starting with the short end and place it in your prepared pan or pans.
Put the lid on the pan or cover your loaf pans with plastic wrap and let the dough rise in a warm, draft-free location until it is nearly up to the lid, about 2 hours.
Thirty minutes before baking, preheat the oven to 350°F.
Bake for 35 to 40 minutes until the internal temperature is 190°F.
Let cool in the pan for 10 minutes, and then cool on a rack completely before slicing.