Step 1: Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.
Step 2: In a large bowl, gently combine the peeled, pitted, and sliced peaches with 1/2 cup granulated sugar, 2 tbsp all-purpose flour, vanilla extract, 1/2 tsp ground cinnamon, 1/4 tsp ground nutmeg, and lemon juice. Toss until the peaches are evenly coated.
Step 3: Pour the peach mixture into the prepared baking dish and spread evenly.
Step 4: In a separate medium bowl, whisk together 1 cup all-purpose flour, rolled oats, light brown sugar, 1/4 cup granulated sugar, 1/2 tsp ground cinnamon, and salt.
Step 5: Add the cold, cubed unsalted butter to the dry ingredients. Using your fingertips, a pastry blender, or two knives, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 6: Evenly sprinkle the crumble topping over the peach filling in the baking dish.
Step 7: Bake for 40-45 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges. If the topping starts to brown too quickly, loosely tent it with aluminum foil.
Step 8: Remove from the oven and let cool for at least 15-20 minutes before serving. Serve warm, optionally with vanilla ice cream or whipped cream.