To make the water roux, whisk together the flour and water in a small saucepan. Cook over medium-high heat, whisking constantly, until thickened. It is ready when the whisk leaves a visible trail as it moves through the roux. Remove from the heat and allow to cool until no longer hot to the touch.

To make the dough, place the flour, cream of tartar, sugar, and yeast in the bowl of a stand mixer, and use a handheld whisk to combine well. Add the salt, and whisk to combine. Add the eggs, butter, milk and roux, and mix on low speed with the dough hook until the dry ingredients are incorporated into the wet. Raise the mixer speed to high and mix again for about 5 minutes. The dough will be quite sticky but should be smooth and stretchy. Spray a silicone spatula lightly with cooking oil spray, and scrape down the sides of the bowl.

Transfer the dough to a lightly oiled bowl or proofing bucket large enough for the dough to rise to double its size, and cover with an oiled piece of plastic wrap (or the oiled top to your proofing bucket). Place the dough in the refrigerator for at least 12 hours and up to 5 days.

On baking day, line a rimmed baking sheet with unbleached parchment paper and set it aside. Remove the dough from the refrigerator and turn it out onto a lightly floured surface. Knead until smoother.

Braid the bread. Once it is braided, carefully transfer the braided dough, already on parchment paper, to a rimmed baking sheet. Next brush the top of the dough carefully but liberally with the egg wash. Cover the braided bread with oiled plastic wrap and allow to rise in a warm, draft-free location for 40 minutes. Brush again with the egg wash, sprinkle with sesame seeds and poppy seeds, and allow to continue to rise uncovered until nearly doubled in size (about another 20 minutes).

Place the bread in the center of a cold oven, and turn the heat to 350° F. Bake for 20 minutes, then turn down the oven temperature to 325° F and bake until the internal temperature of the bread is 185° F on an instant-read thermometer, about another 15 minutes. Allow the bread to cool briefly before serving.