Special equipment: an 18-by-13-inch rimmed baking sheet or jelly roll pan
For the cake: Preheat the oven to 375 degrees F. Coat an 18-by-13-inch rimmed baking sheet or jelly roll pan with cooking spray; line the bottom with parchment paper and spray the parchment.
Beat the cream of tartar and egg whites in a medium bowl with an electric mixer on medium speed until soft peaks form, about 3 minutes. Gradually beat in 1/4 cup of the sugar. Increase the speed to medium high and beat until stiff peaks form, 3 to 4 minutes.
Whisk the egg yolks with the milk, oil, vanilla and remaining 1/2 cup sugar in a large bowl. Sift the flour, cocoa powder, baking powder and salt in a medium bowl; whisk into the yolk mixture until smooth. Stir one-third of the egg white mixture into the batter with a rubber spatula, then gently fold in the remaining egg white mixture in 2 batches. Spread the batter in the prepared baking sheet. Bake until the cake springs back when gently pressed, about 10 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 top with cocoa powder. Starting at the long end, roll up the cake and towel together. Transfer seam-side down to a rack and let cool completely.
For the filling: Whip the cream, corn syrup and vanilla in a medium bowl with an electric mixer until stiff peaks form. Refrigerate until ready to use.
For the glaze: Heat the chocolate, cream, coconut oil and vanilla if using in the top of a double boiler, stirring occasionally, until the chocolate is melted and the mixture is smooth and warm, about 4 minutes. Let cool slightly.
To assemble: Unroll the cake and spread with the filling. With one of the short edges facing you, slice the cake horizontally into 6 strips, then slice in half vertically so you have twelve 3-by-6 1/2-inch strips. Roll the strips to form tight mini jelly rolls. Dust off any excess cocoa powder. Chill for 15 minutes.
Fit a baking sheet with a wire rack. Arrange the rolls on the rack so they are not touching and pour the glaze over them, completely covering the rolls on all sides. Chill at least 15 minutes to set the glaze before serving.
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