Wash and dry the peaches. Then, cut them in half lengthwise and remove the pits. From there, evenly slice the peaches into 1/4-inch thick slices. Add the sliced peaches to a large bowl.
Add the cornstarch, brown sugar, vanilla extract, lemon juice, and pinch of salt to the bowl with the sliced peaches. Next, thoroughly mix these ingredients.
Lightly spray a 9-inch round baking dish, such as a pie pan, with coconut oil. Then, pour the peach mixture into the baking dish.
Make the oat topping. First, use oat flour if you have it, or place 1/2 cup of oats in a blender and blend them into oat flour. (You will need 1/2 cup of oats and 1/2 cup of oat flour.) Add the oats, oat flour, brown sugar, cubed cold butter, cold unsweetened applesauce, cinnamon, nutmeg, salt, and optional chopped nuts to a bowl.
Mix together the ingredients for the topping. Use a fork, your hands, or a pastry cutter to combine the butter with the rest of the ingredients, until a crumbly topping forms.
Once combined, use your hands to crumble and evenly sprinkle the topping over the peaches in the baking dish.
Bake the peach crisp at 350°F for 40-45 minutes, until the topping is golden brown. Once done, let the peach crisp slightly cool before serving. Enjoy or top with a scoop of vanilla ice cream or whipped cream.