Preheat your oven to 190°C (375°F) and lightly grease your baking dish.
Peel the peaches using a peeler or knife, then slice them into 1/2-inch thick pieces and place in a mixing bowl.
Toss the sliced peaches with 2 tablespoons of sugar and a pinch of cinnamon, coating them evenly. Spread the peaches in your prepared baking dish.
In a separate bowl, combine oats, flour, brown sugar, and a pinch of salt. Mix well to distribute evenly.
Add the cold, cubed butter to the dry ingredients. Use a pastry cutter or fork to cut the butter into the mixture until it resembles coarse crumbs.
Evenly sprinkle the crumble topping over the peaches, pressing down gently to help it adhere.
Bake the dish in the oven for 35-40 minutes, until the topping is golden brown and bubbling around the edges. Check at 35 minutes; if the topping is dark but the filling isn't bubbling, cover loosely with foil and continue baking.
Remove the peach crisp from the oven and let it rest for about 10 minutes. This helps it set and makes serving easier.
Serve warm, perhaps with a scoop of vanilla ice cream or a dollop of whipped cream for extra indulgence.