Preheat the oven to 325°F (165°C). Coat a bundt or loaf pan using grease followed by a light dusting of flour so the cake releases easily after baking.
Place sliced peaches into a bowl. Add melted butter, brown sugar, cinnamon, nutmeg, and gently stir until coated. Set this mixture aside.
Beat softened butter together alongside granulated sugar until the texture turns light, fluffy, and pale. Add the eggs one at a time, mixing thoroughly after every addition to keep the batter smooth. Whisk flour, salt, and cinnamon together in another bowl.
Add the dry mixture into the batter in stages, alternating portions of buttermilk. Keep the mixer on low speed and stop once the batter looks uniform. Stir vanilla extract into the mixture.
Use a spatula to gently fold diced peaches throughout the batter. Pour half of the batter into the prepared pan. Spoon the peach cobbler mixture evenly across the surface. Cover using the remaining batter and smooth the top.
Place the pan in the oven and bake for 75 to 85 minutes. Check doneness using a toothpick inserted into the center. If browning happens too fast, loosely cover the top using foil.
Allow the cake to cool for about 15 minutes before turning it out onto a rack. Warm peach preserves slightly, whisk alongside powdered sugar, lemon juice, and milk until smooth, then drizzle over the cooled cake.