For the cinnamon sugar: In a small bowl, mix the sugar, cinnamon and optional nutmeg. Mixture may be made well in advance and will keep for months stored in an airtight container. Feel free to double or triple the recipe if you use it often.
Preheat the oven to 350 degrees F.
Split the English muffins and spread a rounded tablespoon of peanut butter on each half. Layer the apple slices over the peanut butter—I use about 4 thin slices per muffin half. Sprinkle the cinnamon sugar evenly over the top of each muffin half—I use a teaspoon per muffin half.
Place the muffin halves on a baking sheet, and bake for 10 minutes. If desired, you may broil on the low setting until bubbly and lightly caramelized. In this case, watch very closely to avoid burning.)
Let cool for 5 minutes before eating.