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, ½ cup (100 grams) granulated sugar, 2 ¼ teaspoons instant yeast, 2 teaspoons salt
Add the egg, milk, and the starter. Mix on low speed. When it comes together, add the butter cubes.
2 large eggs, ¼ cup (60mL) whole milk, ½ cup (8 tablespoons or 4 ounces) unsalted butter, softened and cut into cubes, 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). Increase the speed to medium and knead for 10 minutes, adding flour as necessary if the dough sticks to the bottom of the mixer. At the end of kneading, the dough should be soft and tacky but not sticky.
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).
I used Wilton color right concentrated food coloring in the following amounts. If you are using a different food coloring, you will need different amounts to get the desired colors.Red: 4 drops red. Orange: 2 drops orange, 2 drops yellow. Yellow: 4 drops yellow. Green: 3 drops yellow. One drop blue. Blue: 4 drops blue. Purple: 4 drops pink. 1 drop blue. 1 drop red. food coloring
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.
Lightly butter a 13" by 4" by 4" Pullman loaf pan, including the lid.
To create the pattern, divide the white dough into six equal parts. Roll each part into a log the length of the pan, and lay four logs into the bottom.
Create a second layer with a red log, two white logs, and the purple log.
The final layer should lay the orange log on top of the red log, then the yellow, green, and blue on top of the purple (see photos).
Put the lid on the pan 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.