Preheat the oven to 350°F. Grease a 9x9 baking dish with baking spray or butter, set aside.
Place the peaches in a large bowl and toss with the sugar until coated. Let the bowl sit at room temperature for 15 minutes.
While the peaches are resting, make the topping. In a medium-sized bowl, stir together the brown sugar, flour, oats, cinnamon, nutmeg, and salt until combined. Add the butter to the small and toss with the flour mixture so the pieces of butter are coated. Using your hands or a pastry cutter, work the mixture until it resembles wet clumpy sand. Any pieces of butter should be about the size of a pea or less. Place this in the fridge until you are ready to assemble the crisp.
Drain the peaches over a large bowl to catch the juice. Take ¼ cup of the juice and place it back in the original large bowl. Whisk the cornstarch, vanilla, cinnamon, and salt with the peach juice until smooth. Add the peaches back in the bowl and toss with the sauce.
Pour the peach mixture into the prepared baking dish. Add the topping. Bake for 40-50 minutes until bubbly and golden brown on top. Let stand for at least 15 minutes before serving.
You will want to use ripe peaches, you can tell if they are ripe by a sweet smell and slightly soft.
This can be kept in the refrigerator for up to 1 week.