Preheat your oven to 350°F (175°C) and lightly grease an 8x8-inch baking dish.

In a large bowl, toss the sliced peaches with lemon juice, vanilla extract, and ¼ cup granulated sugar. Let sit for 10 minutes to allow juices to release.

In a medium bowl, combine the flour, rolled oats, brown sugar, remaining ¼ cup granulated sugar, cinnamon, nutmeg, and salt.

Add the cold, cubed butter to the dry ingredients. Using a pastry cutter or fork, work the butter into the mixture until it resembles coarse crumbs with pea-sized pieces of butter throughout.

Transfer the peach mixture to the prepared baking dish, ensuring an even layer.

Sprinkle the crumb topping evenly over the peaches, covering completely.

Bake in the preheated oven for 30-35 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges.

Remove from the oven and let cool for at least 15 minutes before serving.