In a 9-inch oven-safe skillet over medium heat, melt butter. Add brown sugar, cinnamon, and vanilla. Stir 1–2 minutes until bubbly.
Remove from heat. Layer peach slices in overlapping circles to cover the base.
Mix flour, sugar, baking powder, and salt. In another bowl, whisk milk, egg, butter, and vanilla. Combine wet and dry—don’t overmix.
Preheat oven to 375°F (190°C). Pour batter evenly over peaches.
Bake 20–25 minutes until golden and set.
Cool 2–3 minutes. Loosen edges, cover with plate, flip, and lift skillet after 30 seconds.