Melt the butter in a skillet over medium heat. Add peaches, brown sugar, cinnamon, and vanilla. Cook for 5–7 minutes until softened. Allow to cool.
Combine graham cracker crumbs, oats, brown sugar, cinnamon, and melted butter. Toast in a skillet for 4–5 minutes until lightly golden. Cool completely.
Beat cream cheese, powdered sugar, and vanilla until smooth. In a separate bowl, whip the heavy cream to soft peaks. Fold the whipped cream into the cream cheese mixture.
Layer crumble, cream mixture, and peaches in serving glasses. Repeat the layers until the glasses are full.
Refrigerate for at least 1 hour before serving.
Top with additional peaches and crumble before serving.