Step 1: Preheat your oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish or a 9-inch round pie dish.
Step 2: Prepare the peach filling. In a large bowl, gently combine the sliced peaches, 1/4 cup granulated sugar, flour or cornstarch, vanilla extract, 1/2 teaspoon cinnamon, 1/4 teaspoon nutmeg, and a pinch of salt. Toss everything together until the peaches are evenly coated. Pour the peach mixture into the prepared baking dish and spread evenly.
Step 3: Make the crumble topping. In another medium bowl, whisk together the 1 cup flour, rolled oats, brown sugar, 1/4 cup granulated sugar, 1 teaspoon cinnamon, 1/2 teaspoon nutmeg, and 1/4 teaspoon salt.
Step 4: Add the cold, cubed butter to the dry ingredients. Using your fingertips, a pastry blender, or a fork, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 5: Stir in the chopped pecans (if using). Sprinkle the crumble topping evenly over the peach filling in the baking dish.
Step 6: Bake for 40-50 minutes, or until the topping is golden brown and the peach filling is bubbly and tender when pierced with a fork. If the topping browns too quickly, you can lightly tent it with aluminum foil.
Step 7: Remove from the oven and let the crumble cool for at least 15-20 minutes before serving. This allows the filling to set slightly.