Preheat your oven to 350°F (175°C). In a large mixing bowl, combine sliced peaches with sugar, lemon juice, and cinnamon. Toss gently to coat the fruit evenly and set aside to allow the flavors to meld.
Transfer the fruit mixture into a baking dish, spreading it out into an even layer. This creates the juicy base for your crumble.
In a separate bowl, combine oats, flour, and brown sugar. Use a pastry cutter or fork to cut the cold butter into the mixture until it resembles coarse crumbs. Stir in chopped nuts if using, for added crunch and flavor.
Sprinkle the crumble mixture evenly over the peaches, covering the entire surface. This topping will become crispy and golden as it bakes.
Place the baking dish in the preheated oven and bake for about 40 minutes, or until the topping is golden-brown and the peach juices are bubbling around the edges.
Remove the crumble from the oven and let it cool slightly for 10 minutes. The topping will firm up while cooling, creating a satisfying crunchy texture.
Scoop servings of the warm peach crumble onto plates, and enjoy the contrast of soft fruit and crispy topping. It pairs wonderfully with a dollop of whipped cream or vanilla ice cream if desired.