Start by making the browned butter. Melt butter in a small saucepan over medium heat. Once melted, stir constantly until the butter turns a medium brown and smells toasty like caramel. Pour the butter into a heat safe dish and let cool down most of the way.
Preheat the oven to 350 ℉. Add the peaches, lemon juice, 2 tablespoons of the brown sugar, vanilla bean paste, 1 tablespoon of the browned butter, and cornstarch to an 8–9-inch pie pan or skillet. Stir to combine the ingredients. Sprinkle the remaining tablespoon of brown sugar over the peaches and set aside.
In a medium bowl, stir together all of the crumble ingredients and the remaining browned butter. Stir together with a fork. The mixture should be mostly dry and crumbly. If it seems wet and isn't easy to crumble, add more flour 1 tablespoon at a time. Sprinkle the crumble over the peach filling.
Bake for about 55 minutes. * If using fresh peaches, reduce the bake time about 10 minutes* The crumble should be lightly golden brown and bubbly. Serve warm with a scoop of vanilla bean ice cream.