Preheat the oven to 350°F. Grease and line a 9 x 13-inch rimmed baking pan with parchment paper and set aside.
In a mixing bowl, whisk together the egg yolks, ¼ cup sugar, oil, and milk until smooth. Add the flour and baking powder. Stir until combined
In a clean, dry bowl, begin whipping the egg whites along with the cream of tartar with a whisk attachment on low speed. One a bunch of tiny bubbles appear, it's time to start adding the sugar while slowly increasing the speed. Keep whipping on medium-high speed until thick and they egg whites can hold medium-stiff peaks.
In two batches, add the egg whites to the cake batter. Use a rubber spatula to scoop the batter from the bottom of the bowl and flip it up to the top. Continue to fold together without deflating the egg whites.
Scrape the batter into a lined 9 X 13-inch pan. Use an offset spatula to smooth it out. Bake at 350°F for about 15 minutes, or until the surface of the cake springs back when touched.
When the cake comes out of the oven, dust the top with powdered sugar. Set a clean kitchen or tea towel on top, followed by a cutting board. Carefully flip everything upside down. Remove the baking pan and peal off the parchment. Dust the bottom with powdered sugar. Starting with the short end, carefully roll up the warm cake within the towel. Set aside to cool.