Preheat your oven to 350° F.
Line a 10x15-inch jelly roll pan with parchment paper and lightly grease the surface. Leave an extra inch of paper on each end.
Make the sponge batter by placing the eggs in the bowl of a stand mixer fitted with the whisk attachment, or use a large bowl with a hand mixer. Beat the eggs on high speed for about 3 minutes, until they become very frothy and have doubled in volume.
Gradually add the sugar, a couple tablespoons at a time, and continue beating for 5 to 8 minutes, until the mixture is pale, thick, and has tripled in volume. If you're using a stand mixer, You may not need as much time.
The mixture should reach the “ribbon stage,” meaning it falls in thick ribbons and can briefly hold the shape of a figure “8” when lifted with the beaters.
In a small bowl, whisk together the milk, oil, and vanilla. With the mixer on low speed, slowly pour the mixture into the whipped eggs, mixing gently until just combined.
In another bowl, whisk together the flour, baking powder, and salt. Gently fold the dry ingredients into the egg mixture, being careful not to deflate the batter.
Pour the batter into the prepared jelly roll pan and spread it evenly. Bake for 10 to 12 minutes, or until the cake is golden and springs back lightly when touched.
As soon as the cake is done, run a knife along the edges, then roll up gently in the parchment paper. Let it cool completely, rolled up.