Preheat oven to 325°F Toast almonds in one layer on a baking sheet until lightly browned and fragrant. If they still have skins, rub them in a towel to remove as much as possible. Cool to room temperature. Turn oven off.
Place cooled almonds and 1 tbsp sugar in food processor. Grind into fine powder.
Whisk together flour, cocoa, baking powder and salt.
In a stand mixer with a paddle attachment, beat butter and sugar until fluffy and light. Add vanilla and rum, scrape down sides of the bowl, and beat to combine. Add dry ingredients and almonds and beat on low, just until combined. (You might need to finish with a few swipes of a handheld rubber spatula.) Divide the mixture into two bowls, cover with plastic wrap, and refrigerate 1 hour or until firm enough to work with.
Turn oven back to 325°F Work with one bowl at a time; leave the other in the refrigerator. Line a baking sheet with baker's parchment or Silpat. Scoop out a generous teaspoon of dough and roll into a 3/4" ball. Roll around in remaining sugar, then place on baking sheet. When sheet is full (you should get 30-36 single cookies from each bowl), bake 15 minutes; turn halfway through. Work on the second batch while the first is baking. They are done when puffy and the tops are beginning to crack. Cool 5-10 minutes on the baking sheet, then transfer to a wire rack until room temperature.
Place chocolate and butter in a bowl. Bring cream to a boil over low heat. Pour boiling cream over chocolate and let stand a few minutes. Add liquor and whisk until smooth. Let cool until stiff enough to use. Transfer to a pastry bag for piping (or just use a spoon to fill the cookies - messier but just as effective).
Pair up the cookies by size; set aside the nicer looking ones to be the tops. Divide the ganache evenly amongst the bottom cookies, then cover with the top halves and press gently to spread the ganache out to the edges.