Beat butter at medium speed with an electric mixer until creamy; gradually add brown sugar, beating well. Add eggs, 1 at a time, beating until blended after each addition.
Dissolve coffee granules in 3 tablespoons hot water; stir in milk and vanilla.
Combine flour, baking powder, and salt; add to butter mixture alternately with milk mixture, beginning and ending with flour mixture. Beat at low speed until blended after each addition. Fold in pecans. Pour batter into a greased and floured 10-inch tube pan.
Bake at 325° for 1 hour and 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 to 15 minutes; remove from pan, and cool completely on wire rack.