Divide 2 tablespoons of the butter between 4 (6-ounce) ramekins. Melt the remaining tablespoon of butter and set aside. Evenly divide the brown sugar between the ramekins; sprinkling it into the bottoms of the dishes. Cut each peach into 12 to 14 pieces. Lay the peaches on top of the sugar; evenly dividing them between the dishes and sprinkle with the ginger. Set aside.
In a medium mixing bowl whisk together the flour, baking powder, baking soda and salt. In a separate bowl whisk together the sugar, buttermilk, vanilla extract and 1 tablespoon of melted butter. Add the wet mixture to the dry mixture and stir just until combine. Pour the batter over the peaches; dividing the mixture evenly between the dishes. Place on the middle rack of the oven and bake for 20 to 25 minutes or until the cake reaches an internal temperature of 190 degrees F on an instant-read thermometer.
Remove from the oven to a rack and allow to cool for 5 minutes. Run a knife around the edge of each dish and turn upside down onto a serving plate. Repeat with each cake. Serve immediately with whipped cream or ice cream if desired.