Prepare the muffins: Preheat the oven to 375 degrees F. Mist a 12-cup muffin pan with cooking spray. Warm the cranberries and rum in a small saucepan over medium heat, then remove from the heat and let steep 5 minutes. Drain.
Whisk the flour, baking powder, brown sugar and salt in a medium bowl.
Whisk the butter, eggnog, eggs and vanilla in another bowl. Gently fold into the flour mixture. (The batter will be lumpy; do not overmix.) Fold in the cranberries. Divide the batter evenly among the muffin cups.
Make the topping: Mix the flour, cinnamon, nutmeg, butter, salt and brown sugar in a bowl with your fingertips until it looks like wet sand. Sprinkle generously over the batter.
Bake until the muffins are golden brown and a toothpick inserted into the center comes out clean, about 30 minutes. Cool slightly in the pan, then carefully remove to a rack.