Preheat and prep pan: Preheat the oven to 375°F and line a 12-cup muffin tin with paper liners or grease it well. This keeps the muffins from sticking once baked.
Dice the peaches: Peel and dice the peaches into small, even pieces, about 1/2 inch. Pat them dry with a paper towel to remove extra juice before adding them to the batter.
Mix dry ingredients: In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, and cinnamon until evenly combined. This spreads the leavening throughout so the muffins rise evenly.
Combine wet ingredients: In a separate bowl, whisk the melted butter, milk, egg, and vanilla extract together until smooth. Make sure the butter has cooled slightly so it doesn't cook the egg.
Make the batter: Pour the wet ingredients into the dry ingredients and stir with a spatula just until no dry streaks remain, about 10 strokes. The batter should look thick and slightly lumpy, not smooth.
Fold in peaches: Gently fold the diced peaches into the batter with a few careful strokes so the fruit stays in chunks. Overmixing at this stage breaks down the peaches and turns the batter watery.
Make the crumble topping: In a small bowl, combine the flour, brown sugar, and cinnamon for the crumble. Add the cold, cubed butter and rub it in with your fingers until the mixture looks like coarse, pea-sized crumbs.
Fill the muffin cups: Divide the batter evenly among the 12 muffin cups, filling each about three-quarters full. Sprinkle the crumble topping generously over each one, pressing lightly so it sticks.
Bake until golden: Bake for 18 to 22 minutes, until the tops turn golden brown and a toothpick inserted into the center comes out clean. The crumble should look dry and slightly crisp.
Cool before serving: Let the muffins rest in the pan for 5 minutes, then transfer them to a wire rack to finish cooling. This keeps the bottoms from turning soggy.