Heat oven. Heat the oven to 350°F (180°C, 160°C fan, gas mark 4). Line a 9x13-inch pan with foil or parchment, leaving an overhang on the long sides, and grease lightly.
Mix crust. Stir the crust flour and brown sugar together. Cut in the butter until the mixture looks like damp crumbs.
Bake crust. Press the crumbs evenly into the pan. Bake for 15 minutes, until lightly browned. Keep the oven on.
Make streusel. While the crust bakes, combine the streusel ingredients by hand until they form clumps. Chill for 15 minutes if the kitchen is warm.
Beat filling. Beat the cream cheese and 1/2 cup sugar on medium speed until smooth. Add the eggs one at a time on low speed, then the vanilla. Pour over the warm crust and spread level.
Add apples. Toss the apples with 2 tbsp sugar, the cinnamon and the nutmeg. Spoon over the filling, leaving any juice in the bowl.
Add streusel. Scatter the streusel evenly over the apples.
Bake bars. Bake for 30 minutes, until the edges are set and the center barely jiggles (150°F in the middle). Cover with foil for the last 10 minutes if the top browns too fast.
Drizzle caramel. Drizzle the caramel over the hot bars, or wait until serving for a crisper streusel.
Cool and chill. Cool in the pan on a wire rack for 1 hour, then chill for at least 2 hours. Lift out by the foil and cut into 24 bars, wiping the knife between cuts.