Preheat the oven: Preheat your oven to 350°F and lightly grease a 9x13-inch baking dish with butter or nonstick spray.

Prepare the peaches: Peel and slice the peaches about half an inch thick, then place them in a large bowl. Add the granulated sugar, 3 tablespoons flour, lemon juice, and half a teaspoon of cinnamon, tossing until the slices look evenly coated and glossy.

Spread the filling: Pour the peach mixture into the prepared baking dish, spreading it into an even layer. Set the dish aside while you make the topping.

Mix the dry topping ingredients: In a separate bowl, stir together the oats, 3/4 cup flour, brown sugar, remaining half teaspoon of cinnamon, and salt until well combined.

Cut in the butter: Add the cold cubed butter to the dry mixture and work it in with your fingers or a pastry cutter until coarse crumbs form, about 2 minutes. The mixture should clump together when pressed between your fingers.

Top the peaches: Scatter the crumb topping evenly over the peaches, breaking up any large clumps but keeping the texture uneven rather than smooth.

Bake until golden: Bake for 40 to 45 minutes, until the topping turns deep golden brown and the peach juices bubble thickly around the edges of the dish.

Cool slightly: Remove the crumble from the oven and let it rest for 10 minutes. This allows the juices to thicken slightly so they don't run when scooped.

Serve warm: Scoop the crumble into bowls while still warm, pairing it with vanilla ice cream or a drizzle of cream if you like.