Beat butter and shortening at medium speed with an electric mixer until fluffy; add sugars, beating well. Add eggs, oil, and vanilla, beating until blended.
Combine flour and next 3 ingredients; add to butter mixture, blending well. Cover and chill dough 2 hours or overnight.
Shape dough into 1 1/2" balls. Roll each ball in colored sugar or jimmies in individual bowls, pressing gently, if necessary, to coat balls. Place 2" apart on ungreased baking sheets. Insert craft sticks about 1" into each cookie to resemble a lollipop.
Bake at 350° for 10 to 11 minutes or until set. Let cool 2 minutes on baking sheets; remove cookie pops to wire racks to cool completely.
You'll want to buy several containers of colored sugars and jimmies so you'll have plenty for coating these cookie balls.