Combine warm water with 1 teaspoon of the sugar in a small bowl. Sprinkle the yeast over the top and let sit for 5-10 minutes until foamy.
In the bowl of a stand mixer, add activated yeast, oil, honey, 3 whole eggs, and 1 extra yolk. Whisk until smooth and frothy.
Whisk flour, remaining sugar, and salt together. Add half to the wet ingredients and mix on low speed. Gradually add remaining flour until dough pulls away from the bowl.
Knead with a dough hook on medium speed for 7-8 minutes until smooth and elastic, or knead by hand for 10-12 minutes on a floured surface.
Lightly oil a large bowl, place the dough inside, and turn to coat. Cover with plastic wrap and let rise in a warm spot for 1-1½ hours until doubled in size.
Punch down the dough and divide it in half. Divide each half into 3 equal pieces and roll each into a 14-16 inch long rope.
Lay 3 ropes side by side and pinch the tops together. Braid by crossing the right strand over the middle, then the left over the new middle, repeating to the end. Pinch the ends and tuck under. Repeat with remaining dough.
Loosely cover both braided loaves with plastic wrap and let rise for 45 minutes to 1 hour until puffy. Preheat oven to 350°F (175°C) toward the end of rising.
Whisk the remaining egg with 1 tablespoon water. Brush the egg wash generously over each loaf, getting into the braid crevices, and sprinkle with sesame or poppy seeds if using.
Bake both loaves for 25-30 minutes until deep golden brown, or until an instant-read thermometer inserted into the thickest part reads 190°F (88°C). Tent with foil if browning too quickly.
Let the loaves rest on the baking sheets for 5 minutes, then transfer to a cooling rack to cool completely for about 1 hour before slicing.