Preheat oven to 350°F. Line baking sheets with parchment paper.
Beat the butter and both types of sugar using a hand mixer or a stand mixer fitted with a paddle attachment for 2 minutes until creamy and light. Add eggs and vanilla extract, then stop and scrape the bottom and sides of the bowl so everything mixes together evenly.
1 cup salted butter, ½ cups granulated sugar, 2 large eggs, 1 teaspoon pure vanilla extract, 1 cup (200g) light brown sugar
Add the flour, cocoa powder, baking powder, cornstarch, and salt. Mix on medium-low speed just until everything is evenly combined. You may need to stop and scrape the bottom of the bowl again. Stir in the chocolate chips.
1½ cups (212g) all-purpose flour, 1 cup (128g) cake flour, ¾ cup Dutch process cocoa powder, 1 teaspoon cornstarch, 1 teaspoon baking powder, ½ teaspoon salt, 1½ cups semisweet chocolate chips
Use a large cookie scoop to measure 1/4 cup of dough for each cookie and arrange them on the baking sheet spaces a few inches apart. Refrigerate for 20-30 minutes, then flatten slightly into puck shapes before baking since these don't spread a lot. Arrange them on the prepared baking sheets.
Bake for 10-12 minutes until just set around the edges. Don't overbake. Allow to set up on the baking sheet for 10-15 minutes.
While the cookies bake, mix all peanut butter ingredients together. Roll into 2-3 Tablespoon balls, then press into discs that are slightly smaller than the tops of the cookies. Top each cookie while still warm with the peanut butter mixture.
4 Tablespoons salted butter, 1 cup creamy peanut butter, 2 Tablespoons milk, 1 teaspoon pure vanilla extract, 2½ cups powdered sugar
Gently dollop a spoonful of the melted chocolate frosting on top of the peanut butter filling. Let set completely before serving.
1 cup milk chocolate chips