Preheat oven to 350°F. Line a 9" x 13" pan with parchment paper, leaving about 2 inches of overhang on opposite sides, and spray the parchment and pan with cooking spray.
Melt chocolate and butter: place 6 tablespoons unsalted butter and 6 ounces semisweet chocolate chips in a microwave-safe bowl. Microwave in 30-second intervals, stirring after each interval, until the mixture is smooth. Set aside to cool slightly.
Whisk dry brownie ingredients: in a bowl, whisk together 3/4 cup all-purpose flour, 1/4 teaspoon baking powder, and 1/4 teaspoon salt. Set aside.
Beat brownie wet ingredients: in the bowl of an electric mixer fitted with the whisk attachment (or with a hand mixer), combine 1 cup sugar, 2 large eggs, and 2 teaspoons vanilla extract. Beat on medium speed until pale and slightly thickened, about 3–4 minutes.
Combine brownie batter: add the melted chocolate mixture and 1/4 cup unsweetened cocoa powder to the beaten sugar mixture and mix until combined. Add the flour mixture and beat, scraping down the bowl as needed, until just incorporated.
Bake the brownie base: pour the batter into the prepared pan and smooth the top with a rubber spatula. Bake at 350°F for 15 minutes (the brownie should be partially baked but not fully set).
Make the cheesecake layer: in a clean bowl, beat 16 ounces softened cream cheese until smooth. Add 2 large eggs, 1/4 cup sugar, 2 tablespoons all-purpose flour, 2 tablespoons milk, and 1 teaspoon vanilla extract. Mix on medium speed until the cheesecake batter is smooth, about 3–5 minutes.
Add cheesecake layer and bake: pour the cheesecake mixture over the partially baked brownie layer and smooth the top. Return the pan to the oven and bake at 350°F for 15–20 minutes, until the cheesecake layer is set (the center may still have a slight jiggle but should not be liquid).
Cool completely: remove the pan from the oven and let it cool to room temperature on a wire rack.
Make the Rice Krispies topping: in a small saucepan over low heat, combine 1 cup semisweet chocolate chips, 1 cup peanut butter, and 1/2 cup Nutella. Cook, stirring occasionally, until the chocolate and peanut butter are completely melted and the mixture is smooth. Remove from heat and stir in 3 cups Rice Krispies until the cereal is fully coated.
Finish the bars: spread the Rice Krispies mixture evenly over the cooled cheesecake layer and press gently to level.
Chill to set: refrigerate the assembled pan for at least 2 hours (until the topping is firm).
Cut and serve: use the parchment overhang to lift the slab from the pan. Cut into squares and serve.