Combine yeast, ½ teaspoon sugar, and warm water in a small bowl. Let stand 5 minutes or until yeast mixture is bubbly. Stir sour cream and egg into the yeast mixture and set aside.
Into a food processor bowl with dough blade attachment, add 3 cups of flour, ¼ cup of sugar and salt. Pulse to combine.
Add butter and pulse to combine.
Add yeast mixture through chute while processor is running; keep processing until mixture forms into a ball.
Turn dough out onto a lightly floured surface and knead until smooth and satiny. Add additional flour if necessary. Place dough into buttered bowl and turnover once to butter top. Cover and let rise in a warm place until doubled (about 1 hour.)
Punch down dough and knead dough on lightly floured surface to release air. Place dough on a buttered 14-inch pizza pan or 10×15 jelly-roll pan. Cover and let the dough rest 5 to 10 minutes. Stretch and pat dough out evenly to fit the pan.
Blend together cream cheese and ½ cup sugar until smooth, then blend in egg and lemon peel. Spread mixture over top of dough. Dot the top of the cream cheese mixture with teaspoons of apricot preserves; swirl to create a marbled effect.
Let rise (10 to 15 minutes) until dough is puffy. Bake 25 minutes at 350°F or until crust is golden brown.