In the bowl of a stand mixer, whisk together the milk, sugar, and yeast. Let stand for 5 minutes, until frothy. Once the yeast is frothy, add in the honey and whisk to combine. Add in the egg whites, whisking to combine, followed by the flour and salt. Use the dough hook attachment to knead the flour into the dough until thoroughly combined. Add in the butter and continue to knead until smooth and sticky, about 4 minutes. The dough should come away from the sides of the bowl.
1½ cups warm milk, 3 tablespoons granulated sugar, 2½ teaspoons active dry yeast, ¼ cup honey, 2 egg whites, 4½ cups all-purpose flour, 1 teaspoon kosher salt, 6 tablespoons unsalted butter
Turn the dough out onto a well floured surface. Divide it into 3 equal-sized sections (about 391 grams each). Roll one section of dough into a tight ball and place into a well greased bowl. Cover with a towel to rise. Add red food coloring to one of the remaining sections and green food coloring to the other section. Knead for a few minutes to fully incorporate the color into the dough. Roll each colored section of dough into a tight ball and place into 2 separate, well greased bowls to rise. Cover with a towel and let rise until doubled in size, about 1 hour.
Red food coloring, Green food coloring
Once the dough has risen, turn the uncolored ball of dough out onto a well floured surface. Roll out into a rough rectangle about 7 inches wide and 10 inches long. Carefully transfer the sheet of dough onto a separate baking sheet. Next, roll out the red ball of dough in the same manner. Transfer the red sheet onto the top of the white sheet of dough. Lastly, roll out the green ball of dough. Flip the red and white sheets of dough onto the top of the green sheet of dough with the red being sandwiched between the green on the bottom and the white on the top.
Roll the sheets of dough together into a rectangle about 8 inches wide and 12 inches long. Starting at the 8-inch end, roll the dough into a log. Pinch the edge of the dough together with the log so that it stays together when transferring. Place the dough log into a well greased loaf pan. Spray the top with baking spray. Cover with a towel and set aside to rise for 30 minutes to 1 hour, or until doubled in size. In the last 30 minutes of rising, preheat oven to 350°F.
Place the risen bread into the oven to bake for 1 hour, or until baked through and a toothpick inserted comes out clean (190°F internally). Once baked, remove from the oven and place onto a cooling rack to cool before slicing and serving.