Preheat oven to 350°F. Line baking sheets with parchment paper.
In a large bowl, cream together butter, peanut butter, granulated sugar, and brown sugar until smooth.
Add egg, egg yolk, vanilla, and salt. Mix until fully incorporated.
Add baking soda and flour. Mix just until combined.
Scoop 1 tablespoon portions of dough and roll into balls.
Roll each ball in the granulated sugar.
Place cookies 2 inches apart on prepared baking sheets.
Bake for 12–14 minutes, until puffed and very lightly golden on the bottom.
Immediately press a mini peanut butter cup into the center of each cookie.
Sprinkle lightly with flaky sea salt, if desired.
Cool on the pan for 5 minutes, then transfer to a wire rack to finish cooling.