Preheat the oven to 400°F (20°C) and grease a 9x13 baking dish and set it aside.
If you want to peel your peaches first, follow the next few steps! This peach crisp can use peaches with the skins on as well.
Place fresh peaches into a large pot of boiling water for about 30 seconds and then remove them with tongs. Then place each one in a bowl of ice water and once cool to the touch, remove the skins.
Slice peaches into ½-inch thick slices, then toss in a large bowl with brown sugar, flour, cinnamon and vanilla.
Place a large skillet on the stovetop over medium heat and then cook the peaches for 4-5 minutes. The peaches will soften and create a sauce.
Pour the peach mixture into the previously prepared dish.
In a medium bowl, mix together the ingredients for the crisp topping. Melt unsalted butter and then add it to the bowl of flour, brown sugar and oats.
Combine the ingredients until well mixed and the texture is sand-like.
Pour the crumble topping over the peaches and then place them into the preheated oven.
Bake the crisp for 25 minutes until the peaches are soft and the topping is golden brown. Then remove from the oven and allow to cool for a few minutes.