Beat butter at medium speed with an electric mixer until creamy; gradually beat in 1 1/2 cups sugar. Beat in egg and extract.
Press zucchini between paper towels to remove excess moisture; stir into butter mixture.
Combine flour, baking powder, and cinnamon; gradually add to butter mixture, beating at low speed until blended. Stir in morsels and nuts. Drop by heaping teaspoonfuls onto lightly greased baking sheets.
Bake at 350° for 15 minutes; remove to wire racks to cool. Sprinkle with powdered sugar.