Sift the flour, baking powder, baking soda, and salt together into a small bowl.In a large bowl, cream the butter with an electric mixer on high speed until pale yellow and fluffy. Add the white and brown sugars and continue beating until the grittiness is gone when the mixture is rubbed between your finger and thumb. Add the egg and vanilla and beat on low speed until blended.Add the flour mixture to the butter mixture and, using a wooden spoon, stir until just blended. Do not over-stir. Add the coconut and butterscotch chips, stirring just until blended.
Using a rounded tablespoon, drop the dough onto a lined or non-stick baking sheet, spacing the cookies about 2 inches apart.Bake the cookies for about 15 minutes, or until golden brown around the edges. Let the cookies cool briefly on the baking sheet before transferring them to a wire rack to cool completely. Repeat the process with the remaining dough.