Preheat your oven to 350°F. In a 13x9 baking dish, put in the peaches.
In a big oval baking dish, add the peaches. Mix them up with granulated sugar, brown sugar, cornstarch, lemon juice, lemon zest, vanilla extract, and cinnamon.
In a separate bowl, whisk together the topping ingredients (oats, flour, brown sugar, butter). Pour this mixture evenly over the peaches.
Bake for 30-35 minutes or until the edges are bubbling and the top is golden brown.
Let it cool for 5-10 minutes. If you like, serve it with some ice cream. Enjoy!