Blanch peaches: Bring a pot of water to a boil, drop peaches in for 30 seconds, then plunge into ice water so the skin slides off easily.
Slice and toss: Cut peaches in half, remove the pit, then slice into quarter-inch wedges and place in a large bowl with sugar, lemon juice, and cornstarch.
Butter the dish: Use a 9-by-13-inch baking dish and rub the inside with a small piece of butter.
Mix the topping: In a separate bowl, stir oats, brown sugar, cinnamon, and salt together, then pour melted butter over and mix until every oat is coated.
Layer and spread: Pour peach mixture into the buttered dish, then sprinkle the oat topping evenly across the surface without pressing down.
Bake at 375°F for 35 to 40 minutes until the peach filling bubbles at the edges and the oat topping turns light golden brown.
Cool for 10 minutes: Remove from the oven and let it sit on the counter so the peach juices thicken and the oats firm up.
Scoop and plate: Use a spoon to portion the crisp into bowls, making sure each serving gets peaches and topping together.
Top with cream: Serve warm with vanilla ice cream or a dollop of whipped cream.