Preheat the oven to 350 degrees F.
Halve the muffins and spread a heaping tablespoon of peanut butter on each half. Layer the apple slices on the peanut butter. Mix the sugar, cinnamon and nutmeg together in a small bowl and sprinkle about 2 teaspoons on top of each muffin half.
Put the muffin halves on a baking sheet and bake for 10 minutes. Set the oven to low broil and cook until bubbly and caramelized, about 3 minutes.