Prepare the Apple Filling and the Cheese Topping. Set aside to cool.
In a small bowl, stir together yeast, warm water, and the 1/2 teaspoon sugar. Let stand until bubbly (about 5 minutes).
Meanwhile, in a medium bowl, beat egg, the 4 teaspoons sugar, and the salt until combined. Stir in the half-and-half and butter. Stir in yeast mixture. Gradually stir in enough of the flour to make a moderately soft dough that's not sticky. Cover and let the dough rise in a warm place until doubled (about 45 minutes).
Punch dough down. Shape into a ball. Cover; let rest for 10 minutes. Pat dough over bottom and up the side of a greased 9-inch pie plate. Cover; let rise until nearly doubled (about 30 minutes).
Spread Apple Filling into pie shell. Spread Cheese Topping over filling.
Bake in a 400 degree F oven about 12 minutes or until the bottom of crust is golden brown. If necessary, cover with foil for the last 5 minutes to prevent overbrowning. Cool on wire rack. Serve warm or cool. Store in the refrigerator. Makes 6 to 8 servings.
In a medium saucepan, cook apples in water until apples are very tender. Combine sugar, cornstarch, cinnamon, and nutmeg. Stir into apples. Cook and stir until thickened and bubbly. Cook and stir for 2 minutes more. Cool to room temperature.
In a medium bowl, beat together cottage cheese and cream cheese until well mixed. Add egg yolks and sugar; beat smooth. Beat in vanilla or lemon juice. If necessary, beat in some half-and-half or light cream, a little at a time, to make spreadable.