Heat oven to 375°F. Grease a 10x15-inch jelly roll pan and line with parchment.
Dust a clean kitchen towel generously with powdered sugar and set it near the oven.
Whip eggs and granulated sugar on high until thick, pale, and ribbony, about 4–5 minutes.
Blend in vanilla, milk, and oil on low just until combined.
Sift flour, baking powder, cinnamon, and salt together. Fold into the batter until no dry streaks remain.
Spread batter evenly in the pan and smooth the top. Tap the pan once to release bubbles.
Bake until the cake springs back lightly and edges pull away, 10–12 minutes.
Loosen edges with a knife. Invert the hot cake onto the sugared towel and peel off the parchment.
Roll the cake up in the towel from a short side. Cool on a rack until barely warm, 30 minutes.
Beat cream cheese and butter until perfectly smooth and fluffy.
Add powdered sugar, vanilla, cinnamon, and a pinch of salt. Mix until creamy and spreadable.
Unroll the cooled cake gently. Spread the filling to the edges in an even layer.
Reroll without the towel. Chill 30–60 minutes to set, then dust with powdered sugar, slice, and serve.