Preheat oven to 350 degrees. Line two baking sheets with Silpats (French nonstick baking mats). Sift together flour, cocoa powder, baking powder, and baking soda, and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter, vegetable shortening, granulated sugar, and 1 cup brown sugar on medium speed until light and fluffy, about 2 minutes. Add eggs, one at a time, mixing until fully combined between additions. Add vanilla; beat to combine. Gradually add dry ingredients; mix on low speed until fully combined. Add chocolate chips; mix on low just until combined. Cover bowl with plastic wrap; chill until firm, about 1 hour.
In a small bowl using a rubber spatula, stir together peanut butter and remaining 1/4 cup brown sugar.
Drop 1 tablespoon of dough at a time onto baking sheets, spacing cookies about 2 inches apart. Make a thumbprint in the center of each cookie. Fill thumbprint with 2 teaspoons peanut butter mixture. Top with a second tablespoon of flattened dough. Carefully mold dough to cover the surprise.
Bake until firm, about 12 minutes, rotating halfway through. Transfer baking sheets to wire racks to cool for 5 minutes. Remove cookies from baking sheets, and let cool completely on wire racks.
Peanut filling can be made ahead and stored airtight in refrigerator up to one week. Bring the filling to room temperature before using.