Preheat your oven to 375°F (190°C) and grease a standard muffin tin with non-stick spray or line with paper liners.
In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt until well combined.
In a separate bowl, mix the melted butter, egg, milk, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Gently fold in the diced peaches, cinnamon, and nutmeg until evenly distributed.
Spoon the batter into the prepared muffin tin, filling each cup about 2/3 full.
In a small bowl, mix the brown sugar and coarse sugar together. Sprinkle this mixture evenly over the tops of the batter in each muffin cup.
Bake for 20-25 minutes, or until the tops are golden brown and a toothpick inserted into the center comes out clean.
Allow the cruffins to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.