Preheat the oven to 425°F (220°C). Line a 12-cup muffin pan with silicone or paper liners, or grease each cup with butter or nonstick spray.
Dice 2 medium peaches into small, even pieces, roughly 1/2-inch cubes. Place in a small bowl and toss with 1 tablespoon of flour. Set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg for about 20 seconds.
In a separate large bowl, whisk together the melted butter and brown sugar until no dry sugar streaks remain. Add the eggs one at a time, whisking well after each addition. Whisk in the vanilla extract and buttermilk until smooth and slightly thickened.
Pour the wet mixture into the dry ingredients and fold with a rubber spatula just until no streaks of flour remain. Do not overmix.
Add the flour-coated peaches to the batter and fold gently 8 to 10 times to distribute evenly.
Divide the batter evenly among the muffin cups using a large cookie scoop, filling each about three-quarters full. Mix turbinado sugar with cinnamon and sprinkle over the tops.
Bake at 425°F for 5 minutes, then reduce the temperature to 350°F without opening the oven and continue baking for 15 to 17 minutes until a toothpick comes out clean or with a few moist crumbs.
Let the muffins rest in the pan for 5 minutes, then transfer to a wire cooling rack to finish cooling for at least 10 minutes before serving.