Bloom the yeast: In a large bowl, combine the warm water and active dry yeast with a pinch of the measured sugar. Let sit until foamy, 5–10 minutes.
Mix the wet ingredients: Whisk the remaining sugar with the 2 eggs, 1 egg yolk, and oil until smooth.
Make the dough: Stir the egg mixture into the foamy yeast. Add flour and salt gradually until a shaggy dough forms.
Knead: Knead by hand or with a mixer on medium-low until the dough is smooth, elastic, and slightly tacky, about 6–8 minutes. Add flour 1 tablespoon at a time only if needed.
First rise: Place dough in a lightly oiled bowl, cover, and let rise in a warm spot until doubled in size, 1–2 hours.
Shape: Gently deflate, divide into 3 or 6 equal pieces, and roll each into long even ropes. Pinch the top ends together and braid. Tuck ends under to secure. Transfer to a parchment-lined baking sheet.
First egg wash: Whisk the egg with 1 tablespoon water and brush a thin coat over the braid to prevent drying and start the shine.
Second rise: Let the loaf proof until puffy and about 1 1/2 times its original size, 30–60 minutes. Meanwhile, heat oven to 350°F (175°C).
Final egg wash & seeds: Brush the loaf again for a high gloss. Sprinkle sesame or poppy seeds, if using.
Bake: Bake on the center rack until deeply golden and the internal temperature reaches about 190°F (88°C), 25–35 minutes. Rotate the pan if needed and tent with foil if browning too fast.
Cool: Transfer to a wire rack and cool completely before slicing to set the crumb and keep slices neat.