Place the pecans in a food processor or grinder and grind finely.

In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Stir in the ground pecans. Set aside.

Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Mix in the vanilla.

Reduce mixer speed to low. Add the flour mixture in 3 portions, alternating with 2 portions of the buttermilk. Mix just until combined.

Transfer the batter to prepared pan, and spread evenly. Bake 30-35 minutes, or until a pick inserted into the center comes out clean.

Cool in the pan on a wire rack for 10-15 minutes. Then, transfer the cake from the pan to a wire rack to cool completely.

Using an electric mixer on medium speed, beat the confectioners' sugar and butter until light and fluffy. Mix in the rum and vanilla. Add 2 tablespoons of cream and continue mixing. Add more cream as needed until the frosting is spreadable.

Spread the frosting on the cooled cake. Sprinkle the chopped pecans on top of the frosting.