Preheat oven to 300°F.
In the bowl of food processor, or a mixing bowl, add melted butter, sugar, vanilla, and salt. Pulse or stir to combine. Mix in flour and combine until a soft dough forms. Press dough into an 8-inch tart shell and bake for 15 minutes. Remove from oven and set aside.
Increase oven temperature to 350°F.
Make the filling by combining sliced peaches, flour, brown sugar, and cinnamon in a bowl. Toss to coat peaches. Pour the filling into the baked tart base.
In a food processor (there's no need to clean the bowl from earlier) or mixing bowl, combine oats, brown sugar, flour, salt, and cinnamon. Mix to combine. Add cubes of cold butter and pulse 3-4 times to combine. If you aren't using a food processor, incorporate the butter using a fork or pastry blender. Sprinkle the crumble over the peaches and bake 30-35 minutes.
Allow the tart to cool 30 minutes before removing from tart pan. Serve with vanilla ice cream.