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Step 1
Place 2 pounds chopped russet potatoes, 2 teaspoons of the kosher salt, and 1 teaspoon ground turmeric in a large pot. Add enough cool water to cover by about 1-inch. Bring to a boil over high heat. Reduce the heat to maintain a simmer and cook until the potatoes are fork-tender, 10 to 15 minutes.
Step 2
Meanwhile, heat 1 tablespoon of the olive oil in a 10-inch cast iron or high-sided oven-safe skillet over medium heat until shimmering. Add 1 finely diced medium yellow onion and season with 1/2 teaspoon of the kosher salt and 1/4 teaspoon black pepper. Cook, stirring occasionally, until the onions are translucent and tender, about 5 minutes. Stir in 1 cup finely chopped fresh parsley leaves, 1/2 cup finely chopped fresh chives, and 2 teaspoons finely chopped garlic. Cook until wilted and fragrant, about 1 minute more. Remove the skillet from the heat. Transfer to a large bowl. Reserve the skillet.
Step 3
When the potatoes are ready, drain and return to the pot. Add the onion mixture and, using a flexible spatula, mix and mash the potatoes with the onions and herbs until the potatoes begin to break up into smaller pieces. Let sit until cool to the touch, about 20 minutes. Meanwhile, heat the oven to 350ºF.
Step 4
Place 2 tablespoons of the olive oil in the same skillet. Place in the oven and heat for 5 minutes. Meanwhile, finish making the filling.
Step 5
Add 4 large egg yolks, 3 tablespoons potato starch, the remaining 2 tablespoons olive oil, the remaining 2 teaspoons kosher salt, and a few grinds of black pepper to the potato mixture. Mix until combined.
Step 6
Beat 4 large egg whites with an electric mixer (use the whisk attachment on a stand mixer) on medium speed or by hand until soft peaks form, 1 to 2 minutes. Transfer to the potato mixture and fold together with the flexible spatula until just combined, trying to keep as much air in the egg whites as possible.
Step 7
Carefully remove the skillet from the oven and tilt to coat the bottom with oil. Transfer the potato mixture into the skillet and spread into an even layer. Return the skillet to the oven and bake until the top is golden-brown, the center is set, and the pie begins to pull away from the edges of the pan, about 1 hour.
Step 8
Let cool for 10 minutes. Sprinkle the top with more kosher salt and chopped herbs if desired. Run a thin knife around the edges to loosen. Cut directly in the pan into wedges for serving, or flip out of the pan onto a cutting board before cutting.