Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper.

In a large bowl, use a hand mixer or stand mixer to beat the softened butter, peanut butter, 1/2 cup granulated sugar, and brown sugar together on medium-high speed until light, fluffy, and completely smooth (about 2 minutes).

Add the egg and vanilla extract, beating well until fully incorporated. Scrape down the sides of the bowl.

In a separate medium bowl, whisk together the flour, baking soda, baking powder, and salt.

With the mixer on low speed, slowly add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix!

Place the extra 3 tablespoons of granulated sugar in a small shallow bowl.

Scoop the dough into 1.5-inch balls (about 1.5 tablespoons of dough each). Roll each ball between your hands until smooth, then roll it generously in the granulated sugar.

Place the sugar-coated balls 2 inches apart on the prepared baking sheets.

Use the tines of a fork to press a criss-cross pattern into the top of each cookie, flattening them slightly.

Bake for 10-12 minutes until the edges are just barely golden brown. The centers will look very soft and slightly underbaked.

Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.