Place the butter in a bowl and cream it. Add sugar gradually, mixing until the mixture is light and fluffy. Blend in eggs, one at a time. Blend well and add vanilla. Set aside. Sift the flour with baking powder and salt. Mix with first mixture. Dampen your hands and form a roll with the dough, about 1-1/2 inches in diameter. Wrap in wax paper, and chill at least 2 hours or overnight.
To bake, cut slices (about 1/4 inch thick) from the roll and place on a lightly greased cookie sheet. Sprinkle cookie tops with the "sand" 4 Tbsp sugar mixed with 1 tsp cinnamon. Bake at 375° for 10 - 12 minutes. The cookies should be golden brown.