Preheat the oven to 350°F. Grease a 13- x 9-inch baking pan with vegetable shortening.
Whisk together the flour, baking powder, baking soda, and salt in a medium bowl.
In the bowl of a heavy duty stand mixer fitted with the paddle attachment, beat the butter and sugar at medium speed until light and fluffy.
Add the eggs, one at a time, beating just until the yellow disappears after each addition. Beat in the egg yolks. Add the sour cream and vanilla, and beat until combined.
Add the flour mixture alternately with the milk in three additions, beginning and ending with the flour mixture.
Spread the batter evenly into the prepared pan. Bake for 22 to 25 minutes or until a toothpick inserted in the center comes out clean. Remove from the oven and let cool completely.
Spread the frosting evenly onto the cake and decorate with sprinkles, if desired.