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Step 1
Line the bottom of a shallow airtight container with half of the salt. Make 4 wells using the back of a tablespoon measure, and carefully nestle in the 4 yolks. Gently cover the yolks with the remaining salt (though, you might not need all of it). Cover the container and let the yolks cure for 48 hours in the fridge.
Step 2
On the third day, brush the salt off the yolks—you can gently rinse them under cool water if the salt is clinging stubbornly—and discard the curing salt. Stored in an airtight container, salt-cured egg yolks will keep in the fridge for up to 2 weeks until you’re ready to use them.
Step 3
Heat the oven to 325°F. Grease a bundt pan, and set aside. In a small bowl, stir the flour, baking powder, and salt with a fork.
Step 4
In a stand mixer fitted with the whisk attachment, combine the sugar, eggs, and egg yolks. Whip on medium until thick and glossy, almost like a pale yellow meringue, 2 to 3 minutes. Reduce the speed to low and slowly stream in the hot butter. Crank the speed to medium-high and whip another 2 minutes, or until the butter is well-incorporated. (Some stray bits of salty egg yolk are A-OK.) Reduce speed to low and add dry ingredients in installments, scraping down the sides of the bowl if necessary. As soon as all traces of flour are gone, stop mixing, and transfer batter to the prepared pan. Tap the pan on the counter a few times to remove any air bubbles.
Step 5
Bake for 1 hour and 10 to 1 hour and 20 minutes, or until the cake starts to pull away from the sides of the pan, and bounces back when pressed lightly. Let cool slightly in the pan before unmolding onto a wire rack to cool completely.