Preheat oven to 350 degrees.
Place granulated sugar, brown sugar, and butter in the mixing bowl of an electric mixer and beat on medium-speed until light and fluffy.
Add vanilla and egg and beat well.
In a medium bowl, combine flour, oats, baking powder, and salt. Add to sugar mixture beating on low-speed until blended. Cover and refrigerate 30 minutes.
Combine all ingredients for filling in a medium bowl.
Spray a 9-inch square baking pan with cooking spray and pour peach mixture into pan.
Drop spoonfuls of topping over peaches to completely cover peaches. Bake for 30 to 35 minutes, or until light brown and bubbly.