Preheat the oven to 325 degrees F and line a 10x15-inch jelly roll pan with parchment, leaving one short end slightly overhanging the edge of the pan.
Place the eggs and sugar in a large bowl and whip on medium-high speed until very pale, very fluffy, and tripled in volume (approximately 5 minutes).
Add the flour, cocoa, baking powder, and salt, and fold in gently until almost fully combined.
Stir the melted butter, sour cream, milk, and vanilla together in a small bowl, then fold the mixture into the batter until incorporated.
Transfer the batter to the prepared pan, and bake until springy and no longer glistening (approximately 22 to 28 minutes).
Allow the cake to cool for 5 minutes in the pan, then dust the top of it liberally with powdered sugar and cover with a clean kitchen towel.
Gently roll the cake into a cylinder shape, starting at the shorter side that doesn't have the parchment overhang. (You may want to roll it around something small and cylindrical, such as a child's rolling pin.)
Allow the cake to cool completely in this shape (approximately 2 hours or overnight).
Carefully unroll the cake and spread it with an even layer of filling.
Starting at the short side with the parchment overhang, tightly re-roll the cake back into a cylinder shape and chill for 1 to 2 hours.
Place the chilled Swiss roll on a wire rack set over a baking sheet, and pour the glaze over it, allowing it to fall over the sides and coat the entire roll (you may want to shake or tap it for encouragement).
Allow the glaze to set (approximately 1 hour) in the fridge before slicing.
To make the whipped cream filling
Place the cream cheese and powdered sugar in a large mixing bowl and beat together until smooth.
Scrape the bottom and sides of the bowl with a silicone spatula, then drizzle the cream in a slow, steady stream while continuing to mix on medium speed (stop as needed to scrape again and avoid lumps).
When all the cream has been added, turn the mixer up to medium-high and whip until the filling can hold a stiff peak (approx. 2 to 4 minutes).
To make the chocolate glaze
Heat the cream (either in the microwave or in a pot on the stove) until steamy.
Add the chocolate and corn syrup (if using) and allow the mixture to stand for 5 minutes.