Preheat your oven to 350°F and lightly grease an 8x8-inch baking dish.
Add the sliced peaches, sugar, lemon juice, and vanilla directly to the prepared baking dish. Gently toss everything together until the peaches are evenly coated, then let them sit for about 10 minutes while you prepare the crumble. This gives the peaches time to release some of their juices.
In a medium bowl, combine the brown sugar, salt, rolled oats, flour, cinnamon, baking powder, and butter. Use your hands or a fork to work the butter into the dry ingredients until the mixture comes together into a crumbly texture.
Sprinkle the crumble over the peaches, leaving some of the peaches visible. It does not need to completely cover the fruit.
Bake for 30 to 35 minutes, or until the peaches are bubbling around the edges and the crumble is lightly golden. If the peaches are not bubbling yet or you would like the topping to be more golden, broil for 1 to 3 minutes, watching closely so it does not burn.
Remove the dish from the oven and let it rest for 30 minutes. This gives the peach juices time to thicken into a delicious sauce. Serve warm with a scoop of vanilla ice cream.