Preheat oven to 350 degrees F. Line an 8x8 baking pan with parchment or aluminum foil, and butter the bottom and sides. Set aside.
In a small bowl, combine flour, espresso powder, and salt and whisk together. Set aside.
In a double boiler (or a metal bowl set over a pot of boiling water,) add butter, cocoa, and sugars. Melt and mix until the ingredients form a batter, about 8-10 minutes. The mixture will still be grainy when it's ready.
Remove the bowl from heat and cool slightly. Add the eggs, rum, and vanilla, stirring until well combined.
Stir in flour mixture until just combined. Pour batter into prepared 8x8 baking pan. Bake for 30-35 minutes until a toothpick comes out mostly clean. Allow to cool completely.
In a medium saucepan, whisk together sugar, flour, and nutmeg until well blended. Place saucepan on stove over medium heat and, while whisking, add in eggnog. Whisk until no lumps remain.
Continue to whisk until mixture comes to a low boil and thickens enough to coat the back of a spoon. Remove from heat and cool for 45 minutes-1 hour.
In a stand mixer fitted with a whisk attachment, or with a hand mixer, beat butter for 3-5 minutes until pale and creamy. Pour in cooled eggnog mixture ¼ cup at a time, mixing well between additions, until light and creamy. Don't stress if it looks a bit curdled - just give it a few more minutes and it will come together.
When it's almost ready, add rum and vanilla and whip until incorporated. Spread buttercream evenly in a thick layer over brownies, then sprinkle with ground nutmeg. Refrigerate covered or slice & serve immediately.
Feel free to use a box of brownie mix for this recipe, but add the espresso powder, vanilla, rum, and an extra egg yolk to keep these super fudgy!