Preheat oven to 350°F. Line a 10x15” or 10.5x15” cake/jelly roll pan with foil and spray with floured nonstick cooking spray.
Place eggs in a large bowl or the bowl of an electric mixer. Beat at medium speed with mixer for 3-5 minutes until foamy and yellow. It is very important not to skip this step!
Add sugar and mix for 1 more minute, until the mixture is thickened slightly. Mix in oil, baking powder, salt, and vanilla, then add flour and mix slowly until just combined. Pour into prepared pan, spreading as needed with a spatula. Bake for 10-15 minutes, or until the top is browned and the cake springs back when touched lightly. (Mine took 12 minutes, but all ovens differ.)
While the cake is baking, lay out a clean kitchen towel onto the counter. Spread with about 1/4 cup powdered sugar.
Remove the hot cake from the oven and carefully, using oven mitts so you don’t burn yourself, flip the cake onto the towel. This might make a mess, but that’s okay. Carefully remove the pan and foil (they’re hot!) and then, using the towel, roll up the cake from the short side. The towel will be rolled into the cake. Let this cool completely before continuing.
Note: you can wrap the cooled cake in plastic wrap and let it sit overnight before finishing.
Make the filling: beat cream cheese and powdered sugar until smooth, then add the vanilla and whipping cream and beat until stiff peaks form.
When the cake is cool, carefully unwrap it from the towel. If it cracks, that’s okay.
Brush the cake with the cooled coffee. Evenly spread the filling over the cake and carefully re-roll it, pulling it away from the towel as you go. Wrap in plastic wrap and chill at least 30 minutes.
Make the topping: beat whipped cream with powdered sugar and vanilla until stiff peaks form. For a more authentic tiramisu flavor, add a tablespoon of cooled coffee before beating.
Frost the cake as desired. Dust with cocoa powder before serving.
You can serve immediately or chill until ready to serve. Cover with plastic wrap if storing longer than 2-3 hours.
You can freeze the unfrosted cake for up to one month (or chill it in the refrigerator for up to 1 day) as long as it's wrapped well in plastic wrap. Don't frost until ready to serve.