Combine the yeast, warm water and 1/2 teaspoon sugar in a small bowl or liquid measuring cup. Set aside until slightly foamy, 5 to 10 minutes.
Mix the flour, salt and 2 tablespoons sugar in a stand mixer fitted with the dough hook on medium speed. Add 2 whole eggs, the egg yolk, honey, vegetable oil and yeast mixture. Mix on low speed until a shaggy dough forms. Increase the speed to medium high and knead the dough until soft and smooth but slightly sticky, about 5 minutes (if the dough is too sticky, add 2 more tablespoons flour while kneading). Lightly coat a large bowl with vegetable oil. Put the dough in the bowl, gently turning to coat. Loosely cover with plastic wrap and set aside until nearly doubled in size, 1 to 2 hours.
Transfer the dough to a clean surface and cut into quarters. Lightly dust the surface with flour, then roll each piece of dough into a 12-inch-long log, about 1 1/2 inches in diameter and slightly tapered at the ends. Place the 4 logs side by side a few inches apart. Gather them together at the end farthest from you, pinching the ends together.
Line a baking sheet with parchment paper. To braid the dough, lift the log on the far right over the 2 middle logs. Then take the log on the far left and lift it over the 2 middle logs. Then cross the 2 middle logs over each other. Starting from the right, repeat the process until you reach the other end. Do not braid too tightly; you want the dough to maintain an even shape. Pinch the very ends of the loaf together and tuck underneath. Rock the loaf back and forth a few times to help tighten the braid. Carefully transfer the loaf to the baking sheet. Cover loosely with plastic wrap and set aside until slightly puffed, 1 to 1 1/2 hours.
Position a rack in the middle of the oven; preheat to 375˚ F. Beat the remaining egg and 1/2 teaspoon sugar with a whisk and brush it all over the dough (you will not need all of it). Sprinkle with the seeds. Bake until the bread is dark golden brown all over, 25 to 30 minutes. Transfer to a rack to cool completely.