Preheat oven to 400. Lightly grease a baking sheet or muffin pan (if peaches are small enough to fit into the muffin holes) and set aside.
First, prepare the crumble topping. In a medium bowl whisk together flour, oats, brown sugar, sugar, salt, and cinnamon. Cut in the butter with a pastry knife, or two forks, or with your hands until mixture is crumbly. Set aside.
Next prepare the peaches and filling. Cut ¼ inch off of the top of 5 peaches. Remove and discard the pits (see note) and scoop out the remaining flesh so the peaches are hollowed out (leave about ¼ inch of the outermost flesh/skin intact so they don’t fall apart. ) Dice the flesh (just cut into ½ inch pieces or so) and add to a medium sauce pan. For the remaining peaches, peel the peaches, then cut into wedges, then dice and add those pieces to the pan.
Add butter, brown sugar, and cinnamon to the pan. Saute over medium heat about 5 minutes until peaches are very tender. Divide this mixture between each of the hollowed peaches. Top with the crumble mixture, then place on prepared baking sheet (or muffin tin) and bake for 12-15 minutes. Optional: sprinkle with coarse sea salt after removing from oven.
Top with vanilla ice cream and caramel sauce if desired. Serve immediately.