In a large bowl, use an electric mixer to combine the butter and sugars until light and fluffy. Mix in the eggs, one at a time. Add the vanilla and peanut butter, and mix again. Sift together the flour, baking powder, and salt and add to the batter, mixing only until combined. Fold in the chocolate chunks.
Drop the dough on a baking sheet lined with parchment paper, using a cookie scoop. Dampen your hands, flatten the dough lightly, then press the tines of a wet fork in both directions. Bake for exactly 17 minutes (the cookies will seem underdone.) Do not overbake. Remove from the oven and let cool slightly on the pan, then transfer to a wire rack and let cool completely.