Place yeast, 1 T. sugar, and the warm water in food processor fitted with steel blade. Process mixture briefly and let stand until yeast is foamy, about 5 minutes.
Add flour, butter, salt, and the remaining sugar to processor. With motor running, pour eggs through feed tube. Process just until dough gathers into ball, 15-20 seconds; it will very sticky.
Coat inside of large bowl with vegetable oil or butter. Place dough in bowl and turn to coat entire surface. Cover bowl with oiled plastic wrap and let dough rise in warm place until doubled in bulk, 25-35 minutes.
Punch down dough. Turn out onto lighly floured surface and knead dough 1 minute.
With sharp knife, cut dough in half and use one half as directed in either of my recipes. Keep second half of dough covered at room temperature up to 1 hour and punch down again before using.