Preheat your oven to 350°F (175°C).
In a medium bowl, whisk together the flour, baking soda, and salt.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chocolate chips.
Scoop tablespoon-sized portions of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart.
Press a half peanut butter cup into the center of each cookie dough ball.
Bake for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.