In a large bowl, combine sliced peaches, granulated sugar, 1 tablespoon of flour, vanilla extract, and cinnamon. Toss to coat the peaches evenly and transfer them to the prepared baking dish.
In a separate bowl, mix together the rolled oats, 3/4 cup flour, brown sugar, and salt. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.