1-Prepare the oven and pan: Prepare the oven and pan. Prepare a 9×13 baking tray with parchment paper. Preheat the oven to 350°F or 176°C.
2-Mix the egg yolk mixture: Mix the egg yolk mixture. In a medium mixing bowl, add the egg yolks, 1/4 cup of sugar, salt, vanilla, oil and milk. Mix with a whisk until combined.
3-Sift in the cake flour and baking: Sift in the cake flour and baking powder. Using a fine mesh sieve, sift the cake flour and baking powder into the egg yolk mixture. Whisk to combine. Stop when there are no more lumps or traces of flour.
4-Make the egg white meringue: Make the egg white meringue. In a large mixing bowl, quickly wipe the bowl with a paper towel and some lemon juice or vinegar. Add the egg whites and beat with an electric mixer on high until bubbly and frothy, then add the cream of tartar and beat until the whites are opaque and the bubbles have tightened up. Next, slowly pour the 1/3 cup of sugar in three increments while the mixer is running. Continue beating the egg whites until stiff peaks form or when the egg whites are fluffy, shiny and the egg whites holds its pointed tip when you lift the mixer from the bowl.
5-Combine the egg mixtures: Combine the egg mixtures. Using a rubber spatula, add about 1/3 of the egg white meringue into the egg yolk mixture and very gently fold until mostly mixed. Then add the next 1/3 of the mixture and gently fold and repeat with the remaining third. Be careful to not deflate the air in the mixture by over folding. (Folding is not stirring. You want to gently take the spatula around the edges of the bowl to the bottom of the mixture and scoop upward. Continue until the mixture is combined.)
6-Bake: Bake. Pour the batter into the parchment lined 9×13 inch pan and even out the batter with a spatula. Give the tray a few taps on your work surface to release any large air bubbles. Bake at 350°F or 176°C for 15-17 minutes or until a toothpick inserted in the center comes out clean.
7-Remove and roll: Remove and roll. Once you take the cake out of the oven, quickly flip the cake onto a slightly damp kitchen towel that is larger than the cake on your work surface. Peel off the parchment paper. Begin to roll the cake tightly with the kitchen towel starting with the short side of the cake. Do this very slowly and very gently. Be sure not to squeeze the cake too tightly because this may create cracks. Allow the cake to cool completely rolled up in the towel.
8-Make the whipped cream: Make the whipped cream. Using an electric mixer or your stand mixer with a whisk attachment, whip the heavy cream, sugar and vanilla extract until medium to stiff peaks form.
9-Assemble: Assemble. When the cake has cooled completely, gently unroll the cake and trim the edges. Spread the whipped cream evenly on top using a rubber spatula leaving about 1/2 inch border around the edges. Gently roll the cake back up without the towel. Tightly wrap the cake with plastic wrap and chill the cake in the refrigerator for 1 hour. Then garnish, slice and serve!