Preheat the oven to 350°F and line two large baking sheets with parchment paper and set aside.
In a large bowl or stand mixer fitter with a paddle attachment, cream together 1 cup salted butter, 1 cup granulated sugar, 1 cup light brown sugar, 1⅓ cup peanut butter, ½ cup ground espresso, ½ teaspoon baking powder, ½ teaspoon baking soda, and ½ teaspoon salt until smooth and light in color, about 2 minutes. Scrape down the sides of the bowl as needed.
Beat in 2 large eggs, one at a time, mixing after each addition, then mix in 1 teaspoon vanilla extract and scrape down the sides of the bowl as needed.
Add 1 tablespoon cornstarch to the dough, then add the 3⅓ cups all-purpose flour a little at a time, mixing after each addition just until the flour is mostly incorporated into the dough. Mix the final part of flour in until completely incorporated. If flour is settling at the bottom of the bowl, DO NOT keep mixing in the mixer. Remove the bowl and work the flour in with your hands or a rubber spatula so you don't overmix the dough. Set aside.
Add 1 (9.9oz) bag Reese's piecesto a food processor and pulse for about 15 to 20 seconds; this helps crush the pieces a bit to give them the signature look of these cookies. You can leave them whole, but they can have a hard time sticking to the outside of the dough, so press them in well.
Chop up the 50 Reese's Miniatures peanut butter cups. I think that doing it by hand gives them a look closer to the Gideon's cookies, but you can also pop them in the food processor (after you've already done the Reese's Pieces) and give them a quick chop that way.
Add the chopped Reese's Pieces and peanut butter cups to a medium bowl with 1½ teaspoons ground espresso and mix together with your hands or a rubber spatula. This will help give the coating that signature Gideon's look where the peanut butter cup pieces are like little rounded globs/balls.
Use a #10 cookie scoop or 4 ounces of dough, and roll the dough in the coating mixture; I usually leave a small space uncoated to use as the bottom. You'll need to use your hands to help press the mixture into the dough and reshape as needed. The coating should take these cookies from about 4 ounces to 5.5-6 ounces. You can also make these as 2-ounce cookies, which are perfect for everyday enjoyment, or you can go true Gideon's Bakehouse style and make 6-ounce balls of dough then roll them (their cookies are about a ½ pound each).
Place the cookies about 4 inches apart on the prepared baking sheet and sprinkle with flaky sea salt.
Bake for 14 to 16 minutes. It can be hard to see the cookie itself because of all the toppings to check for doneness, but the cookie should still feel a bit soft when gently pressed in the center.
Allow 4-ounce cookies to cool on the pan for 15 minutes before transferring to a wire rack. Allow 2-ounce cookies to cool for 5 to 7 minutes before transferring. If making 6-ounce cookies, you'll need 18 to 20 minutes.