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

Using a hand mixer or a stand mixer fitted with a paddle attachment, 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. Dough will be thick and soft.

Cover and chill the dough in the refrigerator for 1 hour and up to 3 days. Allow the dough to sit out at room temperature for at least 30 minutes before rolling if chilled longer than a few hours.

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

Scoop cookie dough into large balls, about 3 Tablespoons of dough per cookie, and if desired, roll the balls in granulated sugar. Place 8 balls onto the cookie sheets and press down slightly.

Bake each batch for 14–15 minutes, or until the edges appear set and lightly browned on the sides. The centers will still look very soft.

Cool cookies for 10 minutes on the baking sheet, then transfer to a wire rack to cool completely.

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