Preheat oven to 425°F. Add liners to a 12-cup muffin baking pan. Set aside.
In a large mixing bowl, combine the dry ingredients: flour, baking powder, baking soda, nutmeg, and salt. Whisk to combine. Set aside.
In a separate mixing bowl, whisk together butter and sugar.
Add the eggs one at a time, whisking between each addition.
Add the eggnog, buttermilk, vanilla, and rum extract and whisk to combine.
Make a well, or hole in the center of the dry ingredients. Pour the wet ingredients into the well. Whisk until just combined.
Scoop the batter into the muffin tin, filling the cups about half way. Set aside.
Prepare the crumble by mixing all of the crumble ingredients together in a small mixing bowl. Stir with a fork to combine until nice sized crumbs form.
Sprinkle on top of muffins in pan.
Bake for 5 minutes at 425°F then, keeping the muffins in the oven, reduce the oven temperature to 350°F. Bake for an additional 15-16 minutes or until a toothpick inserted in the center comes out clean.
For the glaze, mix together all glaze ingredients in a small mixing bowl. Whisk until smooth. Drizzle over muffins before serving.