In the bowl of a stand mixture, cream together the butter, peanut butter, and sugars.
Add the eggs, one at a time, then mix in vanilla.
Sprinkle the baking powder and baking soda over and mix in thoroughly.
Stir in the flour until the batter is evenly combined. Chill the dough for 1 hour.
Preheat the oven to 375 and spray cookie sheets with nonstick spray. Pour the 3/4 cup sugar Into a wide bowl or dinner plate.
Roll the dough into 1" balls, roll in sugar, place on cookie sheet 1/2-2" apart. Flatten each one slightly using a fork, making a criss-cross on the top.
Bake for 10-12 minutes. Allow cookies to cool on wire rack.