Mix yeast, sugar and water in small bowl; let stand about 10 minutes.
Meanwhile, in a large bowl, mix eggs, salt, sugar, oil, and two cups flour.
Add yeast mixture to flour mixture.
Add about 1.5 cups flour to the mixture. Dough should start to form a ball.
Place dough on floured surface and knead into a ball, about five minutes.
Place dough into oiled bowl, cover with towel or plastic wrap, and place somewhere warm 60-90 min.
Preheat oven to 375 degrees. Place dough on floured surface, punch it out, and cut in half. Divide each half into three equal pieces and braid (making two challahs). Place on greased cookie sheet (or on parchment paper).
Paint each challah with a mixture of egg yolk plus a little water.
Bake 23-30 min, until bread has risen and is golden brown. Let cool.
More on the cookbook here, and more challah recipes here.