Step 1: Preheat your oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish.
Step 2: In a large bowl, combine the sliced peaches, 1/2 cup granulated sugar, cornstarch, 1/4 teaspoon salt, lemon juice, and 1/2 teaspoon cinnamon (if using). Toss gently to coat the peaches evenly. Pour the peach mixture into the prepared baking dish, spreading it into an even layer.
Step 3: In a separate medium bowl, combine the rolled oats, flour, brown sugar, 1/4 cup granulated sugar, 1/2 teaspoon cinnamon (if using), and 1/4 teaspoon salt. Whisk to combine.
Step 4: Add the cold, cubed butter to the dry topping mixture. Use your fingertips, a pastry blender, or two knives to cut the butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 5: Evenly sprinkle the oat topping over the peach filling in the baking dish. Do not press down firmly; a loose topping will bake up crispier.
Step 6: Place the baking dish on a baking sheet (to catch any overflow) and bake for 40-50 minutes, or until the topping is golden brown and the peach filling is bubbling thickly around the edges. If the topping starts to brown too quickly, you can loosely tent it with aluminum foil.
Step 7: Carefully remove the peach crisp from the oven and let it cool on a wire rack for at least 15-20 minutes before serving. This allows the filling to set and prevents it from being too runny. Serve warm with vanilla ice cream or whipped cream, if desired.