Whisk the flour, baking powder, baking soda, and salt together in a medium bowl. Set aside.

Using a mixer, cream the butter and both sugars together on medium speed until smooth, about 3 minutes. Add the eggs and beat on high until combined, about 1 minute. Scrape down the sides and bottom of the bowl as needed. Add the peanut butter and vanilla, then beat on high until combined.

Add the dry ingredients to the wet ingredients and mix on low until combined. With the mixer running on low speed, add the chocolate chips.

Cover and chill the dough in the refrigerator for 1 hour and up to 3 days.

Preheat oven to 350°F (177°C). Line large baking sheets with parchment paper or silicone baking mats.

Scoop cookie dough into large balls, roll in sugar if desired, and place onto the cookie sheets. Gently press down on each ball to slightly flatten.

Bake each batch for 14-15 minutes, or until the edges are set and lightly browned. The centers will still look soft.

Cool cookies for 10 minutes on the baking sheet. Transfer to wire rack to cool completely.

Cover leftover cookies tightly and store at room temperature for up to 1 week.