Preheat the oven to 425°F. Lightly grease a standard muffin tin or line with 12 muffin cups.
In a mixing bowl, cream together the butter, apple sauce, and sugars with a hand mixer until smooth. Then add the eggs, egg whites, and vanilla, beating to combine.
In a separate bowl, stir together the flour, baking powder, baking soda, nutmeg, and salt.
Stir about one-third of the flour mixture into the butter mixture until incorporated, then stir about one half of the butttermilk into the butter mixture.
Continue alternating between the two until you've mixed in all of the flour mixture and buttermilk (so you begin and end with the flour mixture).
Spoon about 2 Tbsp of the batter into each cup of the prepared pan. Then put about 1 tsp of raspberry preserves in the middle of each cup, and top each with another 2 Tbsp of batter (by the end of this process, the cups should be nearly full).
Bake the muffins for 14-17 minutes, or until they're a pale golden brown and a toothpick inserted into the middle of one of the muffins comes out without any unbaked dough on it. Remove pan from the oven, and let muffins cool for a couple of minutes, or until you can handle them.
While they're cooling, melt the butter for the topping in the microwave and mix together the cinnamon and sugar. Use a pastry brush to spread the top of each muffin with the melted butter, then sprinkle with the cinnamon-sugar mixture on top, using 1/2 tsp per muffin max.