To begin, preheat the oven to 350°F and butter a 9x13 casserole pan. Set up three mixing bowls.
In a large bowl, sift together 1 cup of flour, 1 1/2 teaspoons of baking powder, and 1/4 teaspoon of salt. Separate the egg whites and yolks into the other two bowls.
Using an electric mixer on high speed, beat the egg yolks with 3/4 cup of sugar until they turn a pale yellow, about 2 minutes. Stir in 1/3 cup of milk and 1 teaspoon of vanilla.
Beat the egg whites on high speed until soft peaks form, approximately 1 minute. With the mixer still running, gradually pour in the remaining 1/4 cup of sugar and beat on high speed until the egg whites are stiff but not dry, about 1 more minute.
Pour the egg yolk mixture over the flour mixture and gently combine with a spatula. Carefully fold in the egg white mixture until just combined. Pour the batter into the prepared pan and spread it evenly.
Bake at 350°F for 30-35 minutes or until a toothpick inserted into the center comes out clean.