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Combine the flour, baking powder, and salt in a mixing bowl and stir until thoroughly combined. Put the egg whites in a stand mixer bowl and beat with the wire whip attachment until the whites hold soft peaks. Gently transfer the beaten whites to another bowl and set aside. Rinse the mixer bowl and dry it thoroughly.
Put the butter in the mixer bowl and beat with the paddle until the butter starts to get light and fluffy, about 1 minute. Add the sugar and beat again until fluffy, about 2 more minutes. Add the egg yolks and vanilla, and beat to combine.
Add a third of the flour mixture to the mixer bowl, beat for a moment, then add half the milk and beat for a moment. Add one more third of the flour, beat, then the rest of the milk, then the rest of the flour. Make sure that the flour and milk are entirely incorporated. Then stir a third of the beaten egg whites into the batter. When that is fully incorporated, gently fold in the rest of the beaten egg whites.
Use a pastry bag to pipe the batter into the prepared molds, filling each one just under halfway. Bake for 25 to 30 minutes, or until the cakes start to turn golden and a cake tester or toothpick, when inserted, comes out clean. Allow the cakes to cool entirely.
Unwrap the foil from each cake, and use a knife to make a 2- to 3-inch cut in the bottom of each twinkie. The cut should go about halfway into each cake. Wash the pastry bag and the mixer bowl.
Make the filling. Combine the shortening, butter, salt, powdered sugar, and vanilla in the stand mixer bowl. Beat with the paddle attachment until fluffy, about 3 minutes.
Scoop the filling into a pastry bag and stick the tip into the cut at the bottom of each cake. Keep squeezing the pastry bag until the filling begins to leak out around the tip of the pastry bag. Then it's ready.
Foom temperature: covered container, 3 days
Fridge: filling only, covered container, 10 days
Freezer: cakes, wrapped in foil and a freezer bag, 3 months (thaw at room temperature); filling, freezer-safe container, 3 months (thaw in refrigerator)