Preheat the oven to 375°F. Give the peaches a quick wash and remove the skin. (You can also leave the skin on if you prefer).
Once the skin is removed, slice the peaches around the pit and add them to a bowl. Add peach ingredients to the bowl: white sugar, cornstarch, vanilla extract, cinnamon, nutmeg, and a pinch of salt. Gently mix the ingredients together and set aside.
In a separate bowl or food processor add the crisp topping ingredients: oats, flour, brown sugar, cinnamon, salt, and cold butter. Crumble the ingredients together using one of these methods: with clean hands, with a pastry cutter, or pulsing for a few seconds in a food processor; until a crumble mixture starts to form.
Transfer the peaches into a small-medium size baking dish. Add the crumbled peach crisp topping on top of the peaches. Bake in the preheated oven for 35-40 minutes or until the topping is golden brown. The peaches may start to bubble around the sides of the dish as it bakes.
Carefully remove the crisp from the oven and let it cool for 5-10 minutes. Serve warm by itself, with vanilla ice cream, or with a drizzle of caramel topping. Enjoy!
Notes
I am using a 9.5 x 6.5 x 2 in / 1.5 qt baking dish, but you can use whichever small/medium size one that you have at home. If you would like to use a larger 9 x 13 baking dish, I would suggesting making a larger batch of peach crisp.