In a medium bowl, whisk the all-purpose flour, baking powder, baking soda, and salt until well combined. Set this mixture aside.

Using a hand mixer or stand mixer fitted with a paddle attachment, cream the softened butter and both sugars on medium speed for about 3 minutes until smooth and fluffy. Add the eggs and beat on high for 1 minute until well combined.

Add the creamy peanut butter and vanilla extract to the mixture, beating on high until everything is perfectly combined.

Gradually add the dry ingredients into the wet mixture, mixing on low speed until fully combined. Gently fold in the semi-sweet chocolate chips.

Cover the dough with plastic wrap and chill it in the refrigerator for at least 1 hour, or up to 3 days.

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

Scoop out about 3 tablespoons of cookie dough for each cookie and, if desired, roll them in granulated sugar. Place 8 dough balls onto each prepared baking sheet and gently press each ball to flatten slightly.

Bake the cookies for 14-15 minutes, or until the edges are set and lightly brown. The centers will look soft but will firm up as they cool.

Let the cookies cool on the baking sheet for 10 minutes before transferring them to a wire rack to cool completely.