Position an oven rack in the center and preheat the oven to 350°F. Line two large baking sheets with parchment paper.

In a large mixing bowl, combine the softened butter, creamy peanut butter, brown sugar, and granulated sugar. Beat on medium speed for 2 to 3 minutes, scraping down the sides as needed, until light, fluffy, and pale.

Add the egg and vanilla extract. Beat on medium speed for about 1 minute, until fully incorporated and smooth. Scrape down the bowl again.

In a separate medium bowl, whisk together the flour, baking soda, cornstarch, and salt for about 30 seconds.

With the mixer on low speed, gradually add the dry ingredients to the wet mixture, about one-third at a time. Mix just until the flour streaks disappear and a soft dough forms. Fold in the Reese's Pieces and milk chocolate chips.

Cover the bowl and refrigerate the dough for at least 30 minutes, if desired.

Scoop approximately 2 tablespoons of dough and flatten it slightly in your palm. Place one mini peanut butter cup in the center. Bring the edges of the dough up and around the candy, then roll it between your palms to seal it completely. Repeat with the remaining dough and peanut butter cups.

Place the stuffed dough balls on the prepared baking sheets, spacing them at least 2 inches apart. Press extra Reese's Pieces or chocolate chips onto the tops, if desired.

Bake for 10 to 12 minutes, until the edges are set and lightly golden brown while the centers still appear slightly soft and underdone.

Let the cookies rest on the baking sheets for 5 minutes, then transfer them to a wire cooling rack to cool completely or serve warm.