Line an 8-inch springform pan with parchment paper. Spray the pan lightly with cooking spray to keep the paper in place. Preheat oven to 390 degrees Fahrenheit.
In a mixing bowl, stir together the flour with cocoa powder. Add rest of the ingredients and mix until processed to a crumble.
Press the mixture into the bottom of the pan. Bake for about 12-13 minutes.
Transfer crust with parchment paper to a wire rack and cool completely. If you’re not using spring form let the crust cool completely in the pan before removing/turning over, otherwise, it will crumble.
Line a large jelly-roll or cookie pan with parchment paper (12x16-inch). Spray the pan lightly with cooking spray to keep the paper in place.
Separate the egg whites and yolks. In a large mixing bowl, beat the egg whites and vinegar with an electric mixer on high speed until foamy. Gradually add ½ cup sugar and beat until stiff peak form, about 8-10 minutes.
In a separate bowl, whisk the egg yolks with 1 tablespoon sugar until pale yellow in color. Stir in the milk, oil, and vanilla.
Sift in the flour and cornstarch. Whisk until the mixture is smooth.
Gently mix one part of the egg white mixture (about the ¼ of the whole mixture) with the yolk mixture until creamy. Pour into the bowl with remaining egg whites. Gently fold to blend together to form a smooth and light, batter. Be careful not to deflate the air pockets because the cake might not rise properly.
Gently pour the batter into the prepared pan and spread evenly with an offset spatula. Tap the pan on the counter a few times to break any large air bubbles in the batter. Bake on 325 degrees Fahrenheit until lightly springy when touched, about 20-30 minutes.
Dust a clean, large kitchen towel with the confectioners' sugar and flip the cake out onto the towel with the short side facing you. Remove the parchment paper and roll up the cake in the towel away from you. Set aside to cool.
Pumpkin Orange Filling
Beat cream cheese and butter until smooth and creamy. Add the sugar and beat until smooth and fluffy. Add orange extract, pumpkin puree, pumpkin pie spice and beat until thoroughly combined.
Whisk instant pudding with milk and heavy cream until creamy and thick.
Brown Butter Cream Cheese Frosting
Brown the butter over medium heat. Let it simmer until all the water boils off and it turns a golden brown in color.
Immediately remove from the heat and let sit for 5 minutes. Transfer into a heatproof bowl and chill until it solidifies.
Mix the cooled butter with all the frosting ingredients and beat until smooth and fluffy. If necessary, add just enough milk (1-2 teaspoons at a time) to get the perfect spreadable consistency.
On a large cutting board, unroll the cooled cake so it lays flat. Trim the short ends so they are flat and roll the cake again into a log without the towel. Cut the ends of the log with a serrated knife to help create clean, even layers. Slice the log into 3-4 even strips, using a tape measure if necessary (see Free Tip section for details).
Unroll the strips and spread all but 3 tablespoons of the pumpkin orange filling onto each strip. Top with the chocolate filling. Refrigerate fillings before assembling the cake if they’re too soft.
Roll the first strip of cake into a spiral. Some of the fillings might ooze out but that's OK. Roll the first spiral into the second cake strip. Continue rolling into a spiral until all strips are used. Refrigerate for about 1 hour to set.
Place the cooled crust onto a cake stand or serving platter. Spread 3 tablespoons of the pumpkin orange filling over the crust. Add the rolled cake on the top. The crust might be a bit larger than the rolled cake but after you add the frosting, it will be just right (you can always trim it down if you prefer). Cover with the brown butter cream cheese frosting. Smooth the edge and top of the cake.
Mix in orange food coloring to the remainder of the frosting until desired shade is reached. Use a star tip (or tip of your preference) to pipe frosting around the bottom of the cake and on the top, or decorate as you wish. Refrigerate the cake for about 1 hour or overnight.
Garnish with the chocolate pumpkins if you desire (see the recipe in the post).
Making this cake will take a good portion of your day. Start a day ahead by baking the crust and cake layer and assemble the next.
I would also recommend reading ingredients, directions, and tips a couple of times before starting to bake. It always helps understand all the steps beforehand.
You can slice the cake roll into 4 even strips. It will yield a shorter cake but with more vertical layers.
If the fillings are too soft, refrigerate them to prevent oozing out of the cake, however, make sure they are still easily spreadable.
To cut the cake for serving, keep a large serrated knife dipped in hot water. Clean the knife after each slice and warm it again in the water for the next slice.
You can decorate the cake any way you like and even use a different frosting.
Please keep in mind that nutritional information is a rough estimate and can vary significantly based on products used.