Arrange a rack in center of oven; preheat to 325°. Line a 9" square baking dish with parchment, leaving an overhang on 2 opposite sides.
In a medium bowl, whisk eggs, brownie mix, oil, and water until smooth and glossy. Pour into prepared pan; smooth top.
Bake brownies according to package directions (usually 22 to 28 minutes), or until a tester inserted into the center comes out with a few crumbs attached. Transfer dish to a wire rack and let cool completely.
In a large bowl, using a handheld mixer on medium-high speed, beat mascarpone, cream, and confectioners’ sugar until stiff peaks form, 2 to 3 minutes.
Pour espresso into a shallow bowl. One at a time, quickly dip ladyfingers into espresso and arrange in a single layer over brownies. Spoon mascarpone cream on top; spread in an even layer. Refrigerate to set, at least 2 hours.
Using a fine-mesh sieve, generously dust brownies with cocoa powder. Using parchment overhang, lift out brownies and transfer to a cutting board. Slice into squares.