Preheat the oven to 350°F (180°C) and grease a 9-inch square or similar sized baking dish.
In a large bowl, combine cornstarch and sugars. Add peach slices, vanilla extract, lemon juice, and almond extract. Toss to coat.
Transfer the mixture to the baking dish.
In a medium bowl, combine the old-fashioned oats, brown sugar, butter, flour, cinnamon, and salt.
Mix the ingredients together until large cookie dough like crumbs form. Drop small pieces of the topping evenly over the filling until you used all of the topping.
Bake at 350°F for 45 minutes, until the fruit filling is bubbling and the topping is nicely browned. Let the crisp rest for about 10 minutes before serving. Serve warm with ice cream or whipped cream if desired.