Make the cake: Preheat the oven to 375 degrees F. Coat an 11-by-17-inch rimmed baking sheet or jelly roll pan with cooking spray; line the bottom with parchment paper and spray the parchment. Beat the egg whites and cream of tartar with a mixer on medium speed until soft peaks form, 3 minutes. Gradually beat in 1/4 cup granulated sugar. Increase the speed to medium high; beat until stiff peaks form, 3 to 4 minutes.
Whisk the egg yolks with the remaining 1/2 cup granulated sugar, the oil, milk, vanilla and espresso powder in a large bowl. Sift the flour, cocoa powder, baking powder and salt into a medium bowl; whisk into the yolk mixture until smooth. Stir one-third of the egg whites into the batter with a rubber spatula, then gently fold in the remaining whites in two batches. Spread the batter in the prepared pan; bake until the cake springs back when gently pressed, 10 to 12 minutes. Let cool 5 minutes.
Generously sift cocoa powder over the top of the warm cake and loosen the edges with a knife; lay a clean kitchen towel (not terry cloth) over the cake. Place another baking sheet over the towel and flip the cake with the baking sheets to invert it onto the towel. Remove the top baking sheet and parchment, then dust the cake with cocoa powder. Starting at a short end, roll up the cake and the towel together into a spiral. Transfer seam-side down to a rack and let cool completely.
Meanwhile, make the filling: Beat the butter and salt in a large bowl with a mixer on medium speed until creamy, 2 minutes. Add 1 1/2 cups marshmallow cream and the vanilla; increase the speed to medium high and beat until fluffy, 2 minutes. Reduce the speed to low. Beat in the confectioners' sugar, then the milk, then increase the speed to medium and beat until thick and spreadable.
Gently unroll the cake. Spread the filling over the cake about 1/4 inch from the edges; reroll (without the towel). Trim the ends with a serrated knife, then transfer to a rack set on a baking sheet.
Make the glaze: Microwave the chocolate with the heavy cream in a microwave-safe bowl, stirring every 30 seconds, until smooth. Pour over the cake; spread to coat. Transfer to a platter and refrigerate 15 minutes.
Microwave the remaining 1/4 cup marshmallow cream in a microwave-safe bowl, stirring every 5 seconds, until loose. Drizzle over the cake.