Peel potatoes and cut into 2-inch pieces. Add to a large pot and cover potatoes with about 6 to 8 quarts of water. Season water with kosher salt.

Bring to a boil and cook until potatoes are fork-tender, about 15 to 18 minutes. Use a slotted spoon to remove the potatoes, reserving the water.

Add cooked potatoes to a mixing bowl with ghee, about 1 teaspoon of kosher salt and ½ teaspoon cracked black pepper. Use an electric hand mixer to blend the potatoes until they are whipped and creamy. If your potatoes are not becoming a puree, add a couple tablespoons of the reserved starchy water.

Spoon in or use a piping bag to fill 4 half-pint jars with potato puree, leaving enough room to fit the egg. I filled my jars about two-thirds full of puree.

Crack an egg into each jar and seal the lid on tight. Gently submerge the jars back into the pot and simmer for about 15 minutes, until egg whites are set. Use tongs to remove the jars and a towel to remove the lids.

Garnish each with chopped chives and a heavy pinch of flaky sea salt. Serve.