Beat cream cheese in the bowl of a stand mixer fitted with a paddle attachment on medium speed until smooth, 2 to 3 minutes.
Beat egg whites in a separate bowl on high speed until stiff peaks form, 3 to 5 minutes. Blend in 1 1/2 cups sugar. Fold egg whites into cream cheese, and stir in 1 teaspoon vanilla extract. Pour cream cheese filling into crust.
Bake in the preheated oven until filling is set, about 20 minutes. Remove from oven; set aside.
Increase oven temperature to 475 degrees F (246 degrees C).
Combine sour cream, 2 tablespoons white sugar, and 1/2 teaspoon vanilla extract together in a large bowl. Spread evenly on top of the filling.
Bake in the preheated oven until golden, about 5 minutes. Remove from oven and cool to room temperature, about 45 minutes. Cover with plastic wrap and chill in the refrigerator until firm, at least 2 hours.