Preheat your oven to 350°F (175°C). Line a 10×15-inch jelly roll pan with parchment paper, making sure the paper extends slightly up the sides for easy removal.
In a large mixing bowl, beat the eggs, granulated sugar, and vanilla extract on high speed until light, thick, and fluffy. The mixture should pale in color and fall in ribbons when the whisk is lifted, which helps create a light sponge.
Sift together the all-purpose flour, baking powder, and salt. Gradually fold the dry ingredients into the egg mixture using a spatula, working gently to avoid deflating the batter.
Add the milk and vegetable oil, folding just until the batter is smooth and fully combined. The batter should be airy and pourable.
Pour the batter into the prepared pan and spread it evenly into the corners. Bake for 12–15 minutes, or until the cake springs back lightly when touched and is just set in the center.
While the cake is still warm, carefully turn it out onto a clean kitchen towel dusted lightly with powdered sugar. Gently peel off the parchment paper, then roll the cake up from the short end using the towel to guide it. Let the rolled cake cool completely; this step helps prevent cracking later.
