Preheat oven to 350°F / 177°C.
Spray a 15x10x1-inch jelly roll pan generously with nonstick cooking spray. Line it with parchment paper (trim to fit) and spray paper with nonstick cooking spray. (This will help it to release easily after baking).
Make cake: In a small bowl, whisk together flour, baking powder, and salt. Set aside.
Using a handheld mixer or standing mixer (with the whisk attachment) beat eggs on high speed until very pale and creamy, 5 to 6 minutes.
Reduce mixer speed to low-medium and slowly add sugar with the mixer running. Once the sugar is fully incorporated, slowly add water and then vanilla and continue mixing until smooth.
Gradually add dry ingredients, mixing just until batter is smooth. Pour into prepared pan. Tap the pan lightly on the counter to help remove any bubbles.
Bake just until the edges are light golden and the center springs back gently when pressed, 13 to 15 minutes.
Immediately after baking, run a knife around the edges of the cake to loosen it.
While the cake is still warm, carefully lift the parchment paper and cake out and transfer to a flat surface. Slowly roll cake and parchment paper up from the short end. (I like to use a dishtowel to protect my hand from the hot cake as I roll.)
Transfer rolled cake to a wire rack and let cool completely (at least 30 minutes).
Make filling: While cake cools make filling by using a handheld mixer or standing mixer to beat cream cheese and heavy cream on high until light and fluffy, 3 to 4 minutes. Add ½ cup powdered sugar, Nutella, and cocoa powder. Start the mixer on low and slowly increase speed, beating until the filling is light and fluffy. The filling should be thick and spreadable. Refrigerate for 10 to 15 minutes (this step is important because it will help the filling to hold its shape while rolling the cake).
Set cooled cake out on a flat surface and gently unroll it. Spread filling over the cake, leaving a ½-inch border on all sides.
Carefully roll the cake back up to enclose the filling, removing the parchment paper as you go.
Wrap the cake roll in plastic wrap and refrigerate for at least three hours (and up to a day).
When you're ready to serve, slice a small piece of each of the ends (this makes it look nice and clean for serving). Lightly dust with powdered sugar.
Slice and serve!