Preheat oven to 350°F.

Lightly butter a 9×9-inch baking dish or similar-sized casserole.

In a large bowl, combine the sliced peaches with both sugars, lemon juice, cornstarch, cinnamon, nutmeg (if using), and vanilla.

Toss gently to coat evenly.

Pour into the prepared baking dish.

In a separate bowl, stir together oats, flour, brown sugar, granulated sugar, cinnamon, and salt.

Add the cold butter cubes and use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs.

Sprinkle the topping evenly over the peaches.

Bake for 40–45 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges.

Cool slightly before serving.

Best served warm with vanilla ice cream or whipped cream!