Preheat oven to 190°C (375°F).

Using a stand or handheld mixer, cream butter, peanut butter, and sugars together in a bowl. Beat in the eggs, one at time.

In a separate bowl, sift flour, baking powder, baking soda, and salt. Gradually add into the butter mixture and mix to combine.

Scoop the dough into tablespoonfuls and then roll into a ball. Place on baking sheets with about 3 inches or 8cm between each. Flatten each ball with a fork, making a criss-cross pattern.

Bake for about 10 minutes, or until cookies begin to brown. Take out and place on a cooling rack.