Add the butter, brown sugar, and granulated sugar to a large mixing bowl and beat for 2-3 minutes until creamy and light. Add the peanut butter, eggs, and vanilla extract, then scrape down the bottom and sides of the bowl and beat again to combine.
Once the peanut butter mixture is nice and creamy, add the flour, cornstarch, baking soda, and salt. Mix again just until combined, stopping to scrape the bottom and sides of the bowl again. When making cookie dough, you don't want to overmix after adding the flour because it can result in cookies that aren't as tender and are more crumbly and dry. Try to mix just until combined with the wet ingredients and even leave a few streaks of flour if you will also be stirring in mix-ins like peanut butter chips, chocolate chips, or Reese's Pieces.
Add the Reese's Pieces and peanut butter chips to the bowl of peanut butter cookie dough and stir in by hand or on low speed with your stand mixer just until evenly distributed throughout the dough.
I like to use a large ¼-cup cookie scoop to make big cookies like many of the gourmet cookie shops (e.g. Crumbl, Levain Bakery, etc.) but you can use a medium or small cookie scoop for more reasonably sized cookies if you prefer. Space them a couple inches apart on a baking sheet lined with parchment paper so they have room to spread slightly while they bake or you can freeze balls of cookie dough if you don't anticipate wanting to bake them all right away.
Bake the cookies until just set and starting to turn slightly golden brown around the edges. Don't overbake. The cookies will appear underbaked if you tear into them right away, but they will continue to set up as they cool on the baking sheet for 15 minutes and even more as they cool completely.
For larger ¼-cup size cookies, bake for 10-12 minutes at 350°F. For smaller cookies using a small 2 tablespoon cookie scoop, we recommend baking for 8-10 minutes instead.