Preheat the oven to 350°F (175°C). Peel the peaches and cut them into approximately 1/2-inch-thick slices.

Place the sliced peaches in a large bowl. Add the granulated sugar, lemon juice, 1 teaspoon cinnamon, cornstarch, and vanilla. Toss gently until evenly coated, then leave the mixture for about 10 minutes.

Meanwhile, melt the butter in a medium saucepan over medium heat. Stir constantly as it melts, foams, and gradually develops golden-brown milk solids and a nutty aroma, about 4–5 minutes. Remove it from the heat promptly to prevent burning.

Pour the brown butter into a mixing bowl. Add the rolled oats, flour, brown sugar, remaining 1/2 teaspoon cinnamon, and salt. Stir until a crumbly mixture forms. Fold in the chopped pecans or walnuts if using.

Transfer the peach filling to a 9-inch square baking dish and spread it into an even layer. Scatter the brown butter peach crumble topping evenly over the fruit.

Bake the Peach Crumble Recipe for 35–40 minutes, or until the fruit juices are bubbling around the edges and the oat streusel topping is crisp and golden brown. If the top becomes too dark after about 25 minutes, loosely tent the dish with foil.

Remove from the oven and cool for at least 15 minutes. This resting period helps the peach filling thicken before serving.