Preheat oven to 350ºF. Lightly butter a 10-by-15-inch jelly roll pan; line bottom with parchment paper and spray parchment with cooking spray (note: if you only have a larger cookie sheet with sides, you can use it and not spread the batter to the end)
Sift together flour, 1/4 cup cocoa powder, baking powder, baking soda, and salt and set aside.
In a stand mixer fitted with the paddle attachment, beat eggs and sugar until thick and pale, 3 to 5 minutes. Mix in vanilla and espresso powder.
Gently melt 1/4 cup butter and chopped chocolate in the microwave for 60 to 90 seconds on medium power, stirring every 30 seconds (note: stop heating when the chocolate is almost melted, as the residual heat should be enough to melt it the rest of the way).
With the mixer running on low speed, drizzle the melted chocolate mixture into the beaten egg mixture until evenly incorporated, scraping down the sides of the bowl as necessary.
Sprinkle dry ingredients over top, and mix on low for 10 seconds and then finish by folding into batter using a large rubber spatula; spread into prepared pan, using an offset spatula to spread the batter evenly into the corners.
Bake for 10 to 12 minutes or until the cake springs back when touched with a fingertip. Remove from oven and let cool for 2 minutes, then turn out the cake upside down onto a piece of parchment paper sprinkled lightly with the remaining 1/4 cup cocoa powder (you can also use a clean dish towel); peel away parchment paper from bottom of cake, then gently roll up cake starting with the long side and set the rolled-up cake seam-side down, and let cool completely, at least 30 minutes.
While cake is cooling, prepare the filling by beating cream cheese and 1/4 cup icing sugar together until fluffy. Add hazelnut spread and beat until evenly incorporated, scraping down the sides of the bowl as needed; set aside.
Gently unroll cooled cake, peeling back parchment paper as you go. Spread a thick layer of filling over the top of the cake. Starting with the same side as before, carefully roll up the cake, trying not to let the filling ooze out; set seam side down and refrigerate for at least 30 minutes to allow the filling to set up.
Meanwhile, make the buttercream for the frosting beating the 1 cup butter on medium speed until creamy (about 2-3 minutes) and add 3 1/2 cups icing sugar, cocoa powder, milk; beat on low speed for 30 seconds, then increase to high speed and beat for 2 full minutes (note: add up to 1/2 cup more confectioners' sugar if frosting is too thin or another tbsp of cream if frosting is too thick)
Transfer cake roll to serving platter and, if you are a messy baker, place pieces of parchment strips under the cake to catch an smudges - so you have a clean plate when you remove them! Slather the buttercream all over the cake and cover completely. With a fork, make "tree grooves" by dragging the fork along the length of the roll.
Slice cake with a large chef’s knife, using a single clean slicing motion (do not saw the knife back and forth). Wipe knife clean between slices.