Melt the butter in a medium saucepan over medium heat, stirring constantly until golden brown and nutty, about 5–7 minutes, then let cool slightly.
Preheat oven to 325°F (163°C). In a medium bowl, combine graham cracker crumbs, sugar, and ¼ cup browned butter. Mix until texture resembles wet sand. Press into the bottom of a greased 9-inch springform pan.
Bake crust for 8–10 minutes. Remove and let cool while preparing filling.
In a large bowl, beat softened cream cheese until smooth. Add sugar and beat until fluffy. Mix in sour cream and vanilla extract.
Add eggs one at a time, mixing on low speed just until combined.
Pour in remaining browned butter and fold in half the apple pie filling, chopping apples if desired for easier slicing.
Pour filling into cooled crust and smooth the top.
Bake cheesecake at 325°F for 55–65 minutes until center is slightly jiggly.
Turn off oven, crack door, and let cheesecake cool inside for 1 hour. Then refrigerate at least 4 hours or overnight.
Before serving, spread a layer of Cool Whip or whipped cream on cheesecake. Top with remaining apple pie filling. Drizzle with extra browned butter if desired.
Slice and serve chilled.