In a mixer bowl, combine the flour, yeast, and salt.
4¾ cups (590 grams) unbleached bread flour, 1 teaspoon instant yeast, 2 teaspoons salt
Measure out the water in a large (2 cup is ideal) measuring cup. Add the eggs, egg yolk (reserving the white for the egg wash) oil, and honey, and whisk lightly.
3 whole eggs, 1 egg yolk, ½ cup (110 grams) lukewarm water, ¼ cup canola, safflower, or other neutral vegetable oil, 3 tablespoons honey
Add the wet ingredients to the mixing bowl, and mix on low speed using the paddle attachment until combined.
Switch to the hook attachment and mix on medium speed for 8 to 10 minutes, adding small amounts of water or flour as necessary to get the dough to clear the sides of the bowl. The final dough should be soft and not sticky at all.
Divide the dough into six equal parts and color each dough ball with food coloring.
Form the dough balls into rounds, cover with plastic wrap, and let rise in a warm, draft-free place until about doubled, 1 to 2 hours.
Roll each dough ball into a log about 16 inches long.
Shape a round challah by aligning the middle of three strands perpendicular to the other three in a basketweave pattern (see text for photos), braid each of the four ends together in a loose three-strand braid, and then tuck the three-strand braid under the challah round.
Cover and let rise until puffy, about 1 to 1½ hours.
At least 30 minutes prior to baking, heat the oven to 325°F.
Right before baking, brush the loaf with the reserved egg white (keep for one more brushing).
Bake on a shelf in the lower third of the oven for 10 minutes. Brush one more time with reserved egg wash to ensure coverage of the entire loaf.
Continue baking until internal temperature is 190 to 195°F and the bottom sounds hollow when thumped. This should take about 35 to 45 minutes in total.
Cool for at least one hour before slicing.