Preheat the oven to 350°F. Spray a 9x13-inch baking dish with nonstick cooking spray or line it with parchment paper.
In a large mixing bowl, combine (1) 15.25-ounce box of white cake mix, 1 cup whole milk, ½ cup vegetable oil, 4 egg whites, and 1 teaspoon pure vanilla extract. Beat with a hand or stand mixer on medium speed for 2 minutes, until smooth and creamy. Pour the batter into the prepared dish and spread evenly. Bake for 28 to 32 minutes, or until a toothpick inserted in the center comes out with just a few moist crumbs. Let it cool slightly for 15-20 minutes.
While the cake is still warm, stir the hot espresso and 3 tablespoons of sugar together until dissolved. Use the handle of a wooden spoon to poke holes all over the cake, about an inch apart. Slowly pour the sweetened espresso over the surface, letting it soak into the holes. Refrigerate the cake for 30 minutes while you make the filling.
In a heat-safe bowl, whisk the egg yolks and ¾ cup sugar together until smooth. Set the bowl over a pot of gently simmering water (double boiler method), making sure the bottom doesn’t touch the water. Whisk constantly for 5 to 7 minutes, or until the mixture thickens slightly and reaches about 160°F. Remove from the heat and let the mixture cool to room temperature before adding mascarpone.
Whisk in (1) 8-ounce tub of mascarpone and 1 teaspoon pure vanilla extract until smooth.
In a separate bowl, whip ¾ cup cold heavy cream until stiff peaks form. Gently fold the whipped cream into the mascarpone mixture until fully combined and creamy.
Pipe the mascarpone filling into the poke holes, then spread the remaining filling over the chilled cake using an offset spatula. Try to fill the holes with as much of the filling as possible. Chill the cake for at least 30 minutes before adding frosting.
To make the mascarpone frosting, place (2) 8-ounce tubs of cold mascarpone, 3 tablespoons heavy cream, 1 tablespoon pure vanilla extract, and ¼ teaspoon kosher salt into a large bowl. Beat with a hand or stand mixer until just combined. Gradually add 4 ½ cups of powdered sugar, mixing until the frosting is thick, smooth, and creamy. If the frosting feels too stiff, add another tablespoon of cream until it spreads easily.
Spread the mascarpone frosting evenly over the top of the cake. I like to pipe the frosting over the cake first, then smooth it with an offset spatula.
Chill the cake for 1-2 hours in the refrigerator.
Right before serving, dust the top with unsweetened cocoa powder. Slice and enjoy!