Combine the warm water, active dry yeast, and 1 tablespoon of the sugar in a large mixing bowl, then wait about 5 minutes before continuing. The mixture should look foamy on top, showing that the yeast is active.

Mix in the vegetable oil, 4 eggs, remaining sugar, and salt, reserving 1 egg for the finish later. Add the flour gradually, 1 cup at a time, until a soft dough forms.

Knead the dough on a lightly floured surface until it becomes smooth and supple. The finished dough should feel soft and spring back gently when pressed, rather than sticking heavily to your hands.

Lightly oil the cleaned mixing bowl, return the dough to it, cover, and let it rise in a warm, draft-free place for about 1 hour. When it has nearly doubled, press down the center to release excess gas.

Cover the dough again and let it rise for another 30 minutes before shaping. The dough should look puffy and relaxed, which makes it easier to roll without tearing.

Divide the dough in half for two loaves, then divide each half into 6 equal pieces and roll each piece into a strand about 16 inches long. Arrange the strands side by side and pinch their top ends together firmly.

Braid each loaf by moving the outside right strand over two strands to the left, then moving the second strand from the left to the far right. Continue by moving the outside left strand over two strands to the right, then moving the second strand from the right to the far left.

Repeat that four-move pattern until the braid reaches the end, then tuck the loose end underneath and gently shorten and widen the loaf as needed. The braid should look even from end to end and feel relaxed rather than tightly pulled.

Repeat the shaping with the remaining dough, then place both loaves on a parchment-lined baking sheet with at least 2 inches between them. The space allows the loaves to rise without joining together.

Beat the reserved egg and brush half over the braids, working into the grooves and down the sides. Let the loaves rise in a warm place for another hour, until they look noticeably fuller.

Brush on the remaining egg wash and sprinkle with sesame seeds. The second coat should cover any newly opened areas between the strands.

Bake at 375°F for 30 to 35 minutes. The loaves should be golden brown, sound hollow when tapped underneath, and register 190°F in the center on an instant-read thermometer.