Preheat oven to 375°F. In a large mixing bowl, combine sliced peaches, granulated sugar, lemon juice, vanilla extract, and cinnamon. Toss gently and pour into a greased 9-inch baking dish.
In a separate bowl, mix together flour, oats, brown sugar, baking powder, and salt. Add melted butter and stir until the mixture resembles coarse crumbs.
Sprinkle the crumb mixture evenly over the peaches in the baking dish. Bake for 45 minutes, or until the topping is golden brown and the peach filling is bubbling.