In a small bowl, combine the yeast with the warm water. Add 1 tsp of sugar. Stir to dissolve the yeast. Set aside for 10 minutes or so, until the yeast is activated forming a foamy layer.
In a large mixing bowl, combine the flour, egg yolks, ¼ cup of sugar, salt, and olive oil. Mix with a wooden spoon.
Add the yeast mixture, and mix with the wooden spoon until the dough is too hard to mix.
Transfer the dough to a lightly floured work surface and knead by hand for 10 minutes. If the dough is too sticky as you knead, add a very little bit of flour and continue kneading until the dough is soft and silky.
Place the dough in a large, lightly oiled mixing bowl. Cover with a kitchen cloth and keep it in a warm spot for 1¼ hours, or until the dough has doubled in size.
Punch the dough down and turn it back onto a lightly floured work surface. Divide the dough into three equal pieces (I highly recommend using a scale), then roll each piece into a rope that's about 16 to18 inches long. Braid the three ropes together like you would hair. Squeeze both ends together to complete the braid.
Preheat the oven to 350° F.
Place the braided loaf on a large baking sheet lined with parchment paper. Cover and return to a warm spot for 1 hour allowing it to rise again.
Brush the loaf generously with about 2-3 tablespoon of the egg whites you reserved earlier. Sprinkle the sesame seeds on top.
Bake for 21 minutes. (See recipe notes.)
Let the challah cool before slicing.