PREHEAT OVEN TO 350 DEGREES F.

IN A MEDIUM BOWL, COMBINE FLOUR AND BROWN SUGAR. CUT IN BUTTER WITH A PASTRY BLENDER UNTIL MIXTURE IS CRUMBLY. PRESS EVENLY INTO A 13 BY 9 BY 2-INCH BAKING PAN LINED WITH HEAVY-DUTY ALUMINUM FOIL. BAKE 15 MINUTES OR UNTIL LIGHTLY BROWNED.

IN A LARGE BOWL, BEAT CREAM CHEESE WITH 1/2 CUP SUGAR IN AN ELECTRIC MIXER AT MEDIUM SPEED UNTIL SMOOTH. THEN ADD EGGS, 1 AT A TIME, AND VANILLA. STIR TO COMBINE. POUR OVER WARM CRUST.

IN A SMALL BOWL, STIR TOGETHER CHOPPED APPLES, REMAINING 2 TABLESPOONS SUGAR, CINNAMON, AND NUTMEG. SPOON EVENLY OVER CREAM CHEESE MIXTURE. SPRINKLE EVENLY WITH STREUSEL TOPPING. BAKE 30 MINUTES, OR UNTIL FILLING IS SET. DRIZZLE WITH CARAMEL TOPPING.

STREUSEL TOPPING:

IN A SMALL BOWL, COMBINE ALL INGREDIENTS.