Heat oven to 350° F. Butter an 8-inch square baking pan. In a food processor, finely grind 1 cup of the pecans. Add the flour, baking powder, baking soda, and salt and pulse to combine; set aside.
Using an electric mixer, beat 1 stick of the butter with the brown and granulated sugars until light and fluffy, 5 to 6 minutes. Beat in the eggs one at a time.
Gradually add the pecan mixture, mixing until just incorporated. Stir in the buttermilk and 1 teaspoon of the vanilla. Transfer the batter to the prepared pan.
Bake until golden brown and a toothpick inserted into the center comes out clean, 30 to 35 minutes. Cool for 10 minutes, then transfer to a rack to cool completely.
Using an electric mixer, beat the remaining butter with the confectioners' sugar and cream until fluffy. Beat in the rum and the remaining vanilla. Spread on cake. Chop the remaining pecans and sprinkle on top.
To Bring It: You can make the cake up to 2 days in advance and frost it up to 4 hours before serving. To protect the frosting during your trip, stick a few toothpicks into the top of the cake and make a loose tent with plastic wrap.