Grandma approves... and the kids beg for the last piece!
In a medium bowl, sift flour, baking soda, and baking powder together.
Add 1/2 cup warm butter, sugars, eggs, cooled coffee, and vanilla to the flour mixture and mix with a hand-held mixer until fully combined. (or stir by hand)
In a large bowl, cream butter until smooth, then gradually beat in sugar mixture alternately with heavy whipping cream. Blend in vanilla. Beat until light and fluffy. If necessary, adjust consistency with more whipping cream or sugar.