Whisk the flour, baking soda, and salt in a medium bowl. Set aside.
In a mixer, beat the butter on high for 1 minute until creamy. Add brown sugar and 1/4 cup granulated sugar, beat on medium-high for 2 minutes until smooth.
Add the egg, mix for 1 minute, then add peanut butter and vanilla, beating until combined.
On low speed, add the dry ingredients to the wet mixture, mixing until combined. Chill the dough for 1–2 hours.
Preheat oven to 350°F (177°C) and line baking sheets with parchment or silicone mats.
Roll dough into balls, coat with remaining sugar, place on baking sheets 2 inches apart. Make criss-cross indents with a fork.
Bake for 11–12 minutes until edges are lightly browned. Cool on baking sheet for 5 minutes, then transfer to wire rack to cool completely.
Store cookies at room temperature for up to 1 week.