Preheat the oven to 350. Add the butter to a pan over medium heat. Stir while the butter melts. After a few minutes the butter will begin to bubble. Keep stirring. After a couple more minutes, the butter will foam up, then the foaming will subside and you'll be left with brown, nutty smelling butter. Take off the heat.
Add the brown sugar and stir until combined. Let the mixture cool for at least 10 minutes. After it has cooled, add the eggs, one at a time, stirring between each. Add the vanilla and stir again.
Add flour, cornstarch, baking powder, cinnamon, and salt. Stir until just combined, making sure there are no big lumps. Peel and core the apples, then chop them into small pieces, about 1/4" cubes. Add the apples and stir to combine.
Transfer the mixture to a 9x13" pan lined with parchment paper (if you don't have parchment paper, thoroughly grease the pan). Pour the mixture into the pan and spread it evenly out. Bake for 30-40 minutes, until the top is beginning to brown and the middle is just set.
Let the blondies cool completely before topping with the cheesecake layer. If you are in a hurry, the blondies can cool in the fridge.