1. Preheat oven to 350°F. Add 3 Tbsp. butter to a 9-inch round metal cake pan and place over low heat. Once butter has melted, sprinkle in 1/4 cup brown sugar. Stir until smooth, then spread mixture evenly in pan. Remove from heat and arrange peach slices decoratively in a single layer over brown sugar mixture.
2In a bowl, whisk flour, baking powder, baking soda, cinnamon and salt. In a large bowl, using an electric mixer on medium-high speed, cream remaining 4 Tbsp. butter and 2/3 cup sugar until light, about 3 minutes. Beat in egg and vanilla. Scrape down sides of bowl. Add one-third of flour mixture; mix on low speed until just combined. Mix in half of buttermilk, then another third of flour mixture. Repeat with remaining buttermilk and flour.
3Spread batter gently over peaches, taking care not to displace them. Bake until a toothpick inserted into center of cake comes out clean, 35 to 40 minutes. Let cool for 5 minutes; invert onto a serving plate. Serve warm or at room temperature.