Preheat the oven to 350°F. Line an 8×8-inch baking pan with foil and spray with nonstick cooking spray.
In a large microwave-safe bowl, combine the chocolate chips, butter, peanut butter, and unsweetened chocolate. Heat in the microwave for 1 minute then stir. Continue heating in 30-second bursts, stirring between each burst, until the mixture is melted and smooth but not scorched. Remove from the microwave and let cool slightly.
In a large bowl, use an electric mixer to beat the eggs and sugar on medium-high speed until light and thick, about 3 minutes. Beat in the vanilla extract. Stir in the cooled chocolate mixture with a rubber spatula. Add the flour and salt, folding gently until combined.
Pour half the batter into the prepared baking pan. Place the peanut butter cups on top then cover with the remaining batter. Bake until a tester comes out with moist crumbs still attached, 35 to 40. Do not overbake. Let cool to room temperature. Serve at room temperature.