To make the cake: Preheat the oven to 350° F (180° C) and grease a 13 by 18-inch (33 by 46 cm) cake pan (see Notes) and line the bottom with parchment paper.
In the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites and a pinch of salt at medium-high speed until stiff peaks form.
3 eggs, 1 pinch salt
In a large bowl, whisk together the sugar, avocado oil, reserved egg yolks, flour, baking powder, and orange juice. Fold in the beaten egg whites until just combined. No more white streaks should be visible.
300 grams granulated sugar, 180 milliliters avocado oil, 270 grams all-purpose flour, 8 grams baking powder, 180 milliliters orange juice
Spread the batter on the cake pan. Bake until the top is just starting to turn a golden color and a cake tester or toothpick inserted into the center comes out clean, 18 to 20 minutes. Transfer to a wire rack to cool completely, about 2 hours.
Meanwhile, make the mandarin orange topping: Place the mandarin oranges in a large bowl. In a small bowl, whisk together 2 tablespoons of the mandarin juice with the cornstarch, set aside.
1500 grams mandarin oranges, 500 milliliters orange juice, 25 grams cornstarch
In a small saucepan, heat the remaining 15 ounces (440 ml) of the mandarin juice. Heat to boiling over high heat and whisk in the cornstarch mixture. Continue boiling, while stirring constantly, until thick like pudding, about 1 minute. Remove from the heat and transfer to the bowl with the mandarin oranges.
Add the vanilla and using a rubber spatula, stir until everything is evenly incorporated. Let cool completely.
1 teaspoon pure vanilla extract
To make the frosting: In the bowl of a stand mixer fitted with the whisk attachment, or in a large bowl and using an electric hand mixer, add the powdered sugar, vanilla, and cream and whisk at high speed until stiff peaks form, 2 to 3 minutes. Gently fold in the sour cream until just combined. 40 grams powdered sugar, 2 teaspoons pure vanilla extract, 500 milliliters heavy whipping cream, 750 grams sour cream
To assemble: Evenly distribute the mandarin orange mixture over the cake. Spread on the frosting, sprinkle with cinnamon sugar, and chill in the fridge for 2 hours. Cut into slices and serve. This cake tastes great the next day but doesn’t keep well beyond that and is not freezer friendly.
75 grams granulated sugar, 1 teaspoon ground cinnamon