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Step 1
Arrange a rack in center of oven; preheat to 325°. Cut a 9" circle of parchment to cover bottom of springform pan. Grease pan with butter, dust with flour, and set parchment inside.
Step 2
Sift sugar, baking powder, salt, and remaining 2½ cups flour into a medium bowl. Stir in lemon zest.
Step 3
Whisk egg yolks and vanilla in a medium bowl. Add milk and whisk to combine, then add oil and whisk again to combine.
Step 4
Pour yolk mixture into dry ingredients. Fold batter with a wooden spoon, scraping bottom and sides of bowl, until creamy, glossy, and fully combined (about 6–7 folds).
Step 5
Using an electric mixer on medium-high speed, beat egg whites in a large bowl until soft peaks form. Add cream of tartar and continue to beat until stiff peaks form (do not overbeat; it will dry out the egg whites).
Step 6
Using a large spatula, fold one-third of egg whites into batter to lighten. Fold in remaining egg whites in two additions until batter is bubbly, shiny, and loose.
Step 7
Pour batter into prepared pan and bake cake until a tester inserted into the center comes out clean, 45–50 minutes.
Step 8
Run a very sharp knife between edge of cake and pan. Let cool in pan until cool to the touch, about 1 hour.
Step 9
Carefully remove adjustable body of springform pan and invert cake onto a platter. Peel off parchment. Serve plain or top with whipped cream or icing, if using.