"Create a tiny skillet cake recipe based on this ingredient list, scaled down for a small skillet. Use imperial units only. Include a peach component and browned butter frosting. Keep it concise but complete, with ingredients and step-by-step instructions. Ingredient list to adapt from: 3/4 cup butter, 1 1/4 cups sugar, 3 eggs, 1 teaspoon vanilla extract, 2 cups all-purpose flour, 2 teaspoons baking powder, 1/4 teaspoon salt, 3/4 cup whole milk, 2 1/4 teaspoons lemon juice or white vinegar, 1 tablespoon flour for tossing the batter if needed, 1/2 cup peaches, 2 to 3 tablespoons sugar for the peach syrup, 2 tablespoons water, 1 teaspoon lemon juice optional for the peach syrup, 1/2 cup browned butter for frosting, 1 cup butter for frosting, 3 cups powdered sugar for frosting, 2 teaspoons vanilla for frosting, 2 tablespoons milk for frosting."