MAKE CRUST: Melt butter in a glass 9-inch pie dish in the microwave for 30-60 seconds. Add crushed graham crackers, brown sugar, and salt. Mix until everything is combined well. Press evenly onto the bottom and up the sides of the pie dish. Bake for 10 minutes. Let cool.
MAKE APPLE PIE FILLING: Melt butter in a large skillet. Add apples, lemon juice, brown sugar, cinnamon, nutmeg, corn starch, and water. Cook over medium-low heat for 10 minutes or until apples are almost fork tender, stirring constantly. If sauce gets too thick, add more water 1 Tbsp at a time until desired consistency. Let cool.
MAKE CHEESECAKE FILLING: In the bowl of a stand mixer with the paddle attachment, beat the cream cheese until smooth. Add the sugar and flour. Mix until incorporated. Add the vanilla and egg. Beat until the batter is smooth. Set aside.
MAKE STREUSEL TOPPING: Combine the butter, flour, brown sugar, and salt in a large bowl. Rub together with fingers until mixture clumps together in big crumbs.
ASSEMBLE PIE AND BAKE: Pour the cheesecake filling into the cooked graham cracker crust. Carefully spoon apples evenly over the cheesecake filling. (They may sink a little bit.) Sprinkle streusel topping over the apples. Bake at 350 degrees Fahrenheit for 35-40 minutes until streusel topping browns. Cool completely and REFRIGERATE at least 3 hours before serving. TIP: Use a serrated knife to cut back-and-forth through the crunchy topping and through to the pie.