Combine 1 cup flour, sugar, yeast and salt in large bowl; set aside.
Combine milk and butter in 1-quart saucepan. Heat over low heat until mixture is 120° to 130°F. (Butter does not need to completely melt.)
Gradually beat milk mixture into flour mixture with electric mixer at low speed. Increase speed to medium; beat 2 minutes, scraping down side of bowl once.
Reduce speed to low. Beat in eggs, vanilla and 1 cup flour. Increase speed to medium; beat 2 minutes, scraping down side of bowl once. Stir in enough additional flour, about 2 cups, with wooden spoon to make soft dough.
Turn out dough onto lightly floured surface; flatten slightly. Knead dough about 5 minutes or until smooth and elastic, adding remaining 1/4 cup flour to prevent sticking if necessary.
Shape dough into a ball; place in large greased bowl. Turn dough over so that top is greased. Cover with towel; let rise in warm place 1-1/2 to 2 hours or until doubled in bulk.
Punch down dough. Knead dough on lightly floured surface 1 minute. Cover with towel; let rest 10 minutes.
Refrigerator Sweet Yeast Dough
Prepare Sweet Yeast Dough as directed in steps 1 through 6, except cover with greased plastic wrap; refrigerate 3 to 24 hours. Punch down dough. Knead dough on lightly floured surface 1 to 2 minutes. Cover with towel; let dough rest 20 minutes before shaping and second rising. (Second rising may take up to 1-1/2 hours.)