In a mixer bowl fitted with the paddle attachment, beat the butter and peanut butter on medium speed for 1 minute until creamy. Add brown sugar and granulated sugar and beat on medium speed for about 3 minutes, until fluffy. Beat in the egg, one at a time, then beat in vanilla extract. Add flour mixture and mix just until combined. Do not overmix. Add chocolate chips. The dough will be soft at this point. Chill it for about 1 hour until it's easy to handle.
Roll dough into balls, the size of 2 tablespoons each (mine were about 40 grams each), and place onto the cookie sheets. Bake for about 10 minutes, until cookies just begin to brown at the edges, but the center is still soft. Cookies will appear undone, that's ok. If the cookies are puffy, gently press them down while still warm using a spatula or the back of a spoon but leave them thick. Allow cookies to cool for 10-15 in the cookie sheet until they are easy to transfer without breaking, then gently transfer them to a wire rack to cool completely. Serve cookies warm or at room temperature.