Melt the chocolate, butter, and peanut butter in a small saucepan over medium heat or in a microwave-safe bowl. (If microwaving, heat in 15-second bursts and stir between each.) Once the butter has melted, remove the bowl from the heat and stir until the chocolate melts completely and the mixture is smooth.
In a large mixing bowl, beat together the sugar, eggs, vanilla extract, and espresso powder until well combined.
Pour in the chocolate mixture, baking powder, and salt, then stir to combine. Stir in the flour just until it disappears. The dough will seem very, very soft.
Cover the bowl and chill the dough for at least 3 hours or overnight (it will firm up considerably).
When ready to bake, preheat the oven to 325 degrees F. Line a baking sheet with parchment paper and set aside. Place 1 cup powdered sugar in a wide, shallow bowl.
With a small cookie scoop or spoon, scoop out heaping teaspoon-sized portions of dough and roll into balls that are 1 1/4 inches in diameter.
Place 4-6 balls of dough in the powdered sugar, then gently roll and toss the balls to coat completely (if you do too many balls at once, they will stick together). Shake off the excess sugar, then place them on the prepared baking sheet, leaving 1 1/2 inches between each (the cookies will spread as they bake). Repeat with remaining cookies.
Bake for 10 minutes, rotating the pan halfway through the baking time by turning it 180 degrees, and if baking multiple cookie sheets at once, switching the top and bottom pan positions. When the tops are dry and just set, remove the cookies from the oven. Let cool on the baking sheets for 2 minutes, then transfer to a wire rack to cool completely.
Notes
TO STORE: Leftover chocolate peanut butter cookies can be stored in an airtight container at room temperature for 3 days.
TO FREEZE: Store cookies in the freezer for up to 1 month in a covered container. Let thaw before serving (or not—I won't judge).