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Preheat the oven to 325°F with a rack in the center. Lightly grease an 8" round pan and line the bottom with a parchment round or reusable silicone liner.
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To make the cake: In a medium bowl, vigorously whisk the sugar, oil, egg, salt, and extracts together for a full 1 minute. The mixture will thicken and become pale yellow in color.
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In a microwave-safe bowl or liquid measuring cup, heat the milk and butter in 30 second increments until the butter is melted. Alternatively, combine the milk and butter in a small saucepan and warm over low heat, stirring until the butter is melted. Slowly pour the hot liquid over the egg mixture and then whisk until smooth.
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Sift the flour, cornstarch, and baking powder into the bowl and whisk until smooth; a few small lumps are OK. The batter will be very thin.
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Pour the batter into the prepared pan and bake for 34 to 38 minutes, until the center of the cake springs back when gently pressed and a toothpick or thin knife inserted into the center comes out clean.
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Remove the cake from the oven and allow it to cool in the pan for 15 minutes. Run a small offset spatula or dull knife around the edge of the cake to loosen it, turn it out onto a wire rack, and allow it to cool completely before frosting.
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To make the frosting: In a medium bowl, beat the confectioners’ sugar, butter, cocoa, vanilla, and salt on low speed until crumbly.
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Add 2 tablespoons (28g) of the milk and increase the speed to medium-high, beating until smooth. Add the remaining 1 tablespoon milk if the frosting feels stiff, then continue to beat until the frosting is light and fluffy in consistency. Stop and scrape down the sides of the bowl as needed.
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Once the cake is cool, spread the frosting evenly over the top of the cake. There will be enough frosting to cover the top and sides, if you like. Add sprinkles or your desired garnish.
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Storage information: Store any leftover frosted cake, covered, at room temperature for up to 4 days. Unfrosted vanilla cake can be frozen for longer storage.
