Preheat oven to 375°F (190°C). Generously grease a half sheet pan (18×13 inches) or jelly roll pan (15×10 inches) with butter. Dust with flour, tilting pan to coat completely, then tap out excess. This double protection prevents sticking.

In a large mixing bowl, whisk together flour, corn starch, sugar, baking soda, and salt until well combined. Set aside while preparing wet ingredients. The dry mixture can sit for up to 2 hours if prepping ahead.

In a small bowl, whisk together eggs, sour cream, almond extract, and vanilla extract until completely smooth and pale. The mixture should have no streaks of sour cream visible. Set aside.

Place butter, oil, and water in a medium saucepan over medium-high heat. Bring to a rolling boil with large, vigorous bubbles breaking the surface, not just small bubbles around edges. This should take 3-4 minutes.

Immediately pour the boiling butter mixture over the flour mixture. Stir quickly but gently - the batter will be lumpy at first, which is normal. Add the egg mixture and stir just until combined. The final batter will be thin like pancake batter.

Pour batter into prepared pan - it will naturally level itself. Bake for 18-20 minutes for half sheet pan, 20-22 minutes for jelly roll pan. The cake is done when center springs back lightly when touched and edges just pull away from sides.

When cake has 5 minutes left to bake, start the frosting. Melt butter in a medium saucepan over medium heat. Add milk and bring to a simmer. Remove from heat and whisk in powdered sugar, almond extract, and salt until smooth.

If using nuts, stir sliced almonds or chopped pecans into the warm frosting until completely coated. The nuts will toast slightly from the heat of the frosting.

Remove cake from oven and let cool for exactly 20 minutes - warm but not steaming. Pour warm frosting over warm cake, spreading quickly with offset spatula. The frosting will melt slightly into the cake, creating the signature glossy finish.

Let cake cool completely, about 1 hour, until frosting sets with characteristic crackly top. Cut into squares and serve. Store covered at room temperature for up to 3 days.