Preheat oven to 350 F. Line muffin tin with foil-lined muffin paper cups.
In each muffin cup, place 1/2 tsp brown sugar & 1 full slice of peach.
Cream butter & remaining sugars until fluffy. Add egg & vanilla. Mix well. Whisk together flour, baking soda, salt, cornstarch & cinnamon. Gradually add to wet ingredients.
Divide dough into 12-14 portions & roll each into a ball. Place a cookie dough ball on top of each peach slice in the muffin cups..
Bake for 12–15 minutes. Cool 5 mins, then gently flip cookies out & remove paper cups. Serve peach side up warm, chilled or at room temperature. Store in airtight container.