Preheat oven to 375°F and grease a 12-cup muffin pan.
Whisk flour, baking powder, baking soda, salt, and nutmeg together.
Cream butter and sugar for 2 to 3 minutes until fluffy.
Beat in eggs one at a time, then stir in vanilla.
Alternate adding dry ingredients and milk in three additions, mixing until just combined.
Fill muffin cups two-thirds full.
Bake 18 to 20 minutes until golden and a toothpick comes out clean.
Cool 10 minutes in the pan, then move to a wire rack to cool completely.
Fill a piping bag with raspberry jam.
Inject 1 to 1½ teaspoons of jam into the center of each muffin.
Melt butter in a small bowl.
Dip each muffin top in melted butter.
Roll buttered tops in cinnamon sugar and set on the rack to firm up.