Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, beat together the peanut butter, brown sugar, granulated sugar, and softened butter using a wooden spoon or spatula until smooth and creamy, about 1 minute.
Add the egg, egg yolk, and vanilla extract to the peanut butter mixture. Stir until completely combined and the mixture looks glossy.
Add the flour, baking soda, and salt directly to the bowl. Stir just until no dry streaks remain, being careful not to overmix. The dough will be thick and slightly sticky.
Scoop the dough into 2-tablespoon portions and roll into balls. Place them 3 inches apart on the prepared baking sheets.
Dip a fork into granulated sugar and press a crisscross pattern into each cookie ball, flattening them to about 1/2-inch thickness. Re-dip the fork in sugar between each cookie.
Bake for 10-12 minutes, until the edges are lightly golden and set but the centers still look soft and slightly underdone. Do not overbake.
Let the cookies cool on the baking sheet for 5 minutes to finish setting, then transfer to a wire rack to cool completely. They will firm up as they cool while staying wonderfully chewy in the center.
