Start by preheating your oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners, or give them a light coating of cooking spray. I prefer liners since the peaches can sometimes stick to the pan.
In a large bowl, mash bananas until they’re mostly smooth but still have some small lumps. You want really ripe bananas here, with lots of brown spots on the skin.
Peel and dice peaches into small chunks, about 1/4 inch pieces. If they’re really juicy, pat them gently with a paper towel – this helps prevent soggy muffins. Leave them on the paper towel while you mix the rest.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg. The spices might seem like a small amount, but they really bring out the fruit flavors without overwhelming them.
Back to banana bowl – add both sugars, eggs, vegetable oil, milk, and vanilla. Mix until well combined and the sugars are mostly dissolved. The mixture might look a bit curdled, but that’s totally normal.
Add dry ingredients to the wet mixture in two portions, stirring gently with a rubber spatula just until you don’t see any more dry flour. You’ll notice the batter getting pretty thick – that’s exactly what you want.
Fold in diced peaches with just a few gentle strokes. The batter should be thick but still scoopable.
Divide the batter between muffin cups – they should be about 3/4 full.
Bake for 20-22 minutes, or until the tops are lightly golden brown and a toothpick inserted into the center comes out clean or with just a few moist crumbs. The tops should spring back when you gently press them with your finger.
Let the muffins cool in the pan for about 5 minutes – they’re pretty delicate when hot.