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

In a large bowl using a handheld mixer or stand mixer with paddle attachment, cream the butter, brown sugar, and granulated sugar together on medium speed until combined. On low speed, beat in the peanut butter, egg, and vanilla extract. Turn the mixer up to high and beat until light in color and smooth, about 1-2 minutes. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed. On low speed, slowly pour in the dry ingredients. Mix until combined.

Cover tightly and chill the cookie dough for at least 1 hour and up to 3 days.

Preheat the oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats. (Always recommended for cookies.) Set aside.

Remove cookie dough from the refrigerator. Measure cookies to be 1.5 Tablespoons each. I recommend this medium cookie scoop. Pour extra 1/2 cup granulated sugar for the topping in a bowl. Roll each cookie dough ball in the granulated sugar and arrange 3 inches apart on the baking sheets.

Bake for 11-13 minutes. Cookies will look very soft. Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes. Working quickly, press 1 peanut butter cup into the center of each cookie. Quickly transfer the cookies to a freezer-safe dish (I use a plate) and freeze for 10-15 minutes or until the peanut butter cup has set. Some of the peanut butter cups will melt slightly—that’s ok.