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.
