Before you start: allow eggs, cream cheese, and ½ cup butter to get to room temperature. Makes for better baking.
Preheat oven to 350°F.
Combine flour and sugar in a medium bowl or food processor. Add chunks of the 1 cup cold butter and pulse until just combined or use a pastry cutter to cut the butter in. It's done when the mixture is crumbly and looks like sand.
Line a 9x13 pyrex dish with aluminum foil and grease. Press the crust dough into the dish and bake for 10-15 minutes until lightly browned.
While the crust bakes, beat the cream cheese and sugar together on medium-high. Add one egg at a time and then vanilla, beating until just combined.
In a mixing bowl, mix the streusel: combine the flour, oats, and sugar. Cut in the butter in the same way you did for the crust - either with a food processor or a pastry cutter.
Peel, core, and dice the apples. Toss with cinnamon, nutmeg, and remaining sugar.
When the crust comes out of the oven, pour the cheesecake over. Top with apple mixture and streusel and bake, 30-40 minutes until filling is set.
After 35-40 minutes, if the dish has lost most of its jiggle but the top isn't brown enough, switch the oven to broil for 5 minutes. Watch closely to not burn.
When the cheesecake is done, drizzle caramel generously on top.
Let cool on the counter and then refrigerate until fully chilled, ideally overnight. Once chilled, cut into 2-inch squares. Serve cold.