In a medium bowl, simply whisk together the flour, cocoa powder, baking powder, and salt. Set this dry mixture aside.
Gently melt the chopped semisweet chocolate in a heatproof bowl. You can use a microwave in 30-second intervals, stirring well between each, until it's smooth and luscious. In a separate small bowl, lightly beat the eggs with the vanilla. Sprinkle the instant espresso powder over this egg mixture and let it sit for a moment to dissolve.
Using an electric mixer fitted with a paddle attachment, beat the softened butter on medium speed until it's wonderfully smooth and creamy (about 15 seconds). Add both the light brown sugar and granulated sugar, mixing until they are fully combined and granular (about 45 seconds). Reduce the mixer speed to low, then gradually beat in the egg mixture until it's well incorporated (about 45 seconds). Finally, stream in the melted chocolate and continue beating until everything is beautifully blended (about 40 seconds), scraping down the sides of the bowl with a rubber spatula to ensure thorough mixing.
With the mixer still on low speed, add the dry ingredients to the wet mixture, mixing just until they are barely incorporated. Stir in half of the mini peanut butter cups until the dough just comes together, being careful not to overmix. Cover the bowl with plastic wrap and let the dough rest at room temperature for about 30 minutes. This crucial step allows the chocolate to cool and the dough to firm up, making it perfectly scoopable!
While the dough rests, preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper. Use a 1 ¾-inch cookie scoop to place dough balls onto the prepared baking sheets, leaving about 1 ½ inches between each. For an extra touch of deliciousness, gently press a few more mini peanut butter cups into the top of each dough ball.
Bake the cookies for 10-12 minutes. You'll know they're ready when the edges are just beginning to set, but the centers still look delightfully soft. This ensures a wonderfully chewy and fudgy cookie! Make sure to rotate the sheets halfway through baking for even results. Let the cookies cool on the baking sheets for about 10 minutes before carefully transferring them to wire racks to cool completely.