Step 1

Arrange a rack about 4 inches from the broiler element, then heat the broiler to high.

Step 2

Meanwhile, grate 8 ounces sharp cheddar cheese on the large holes of a box grater (about 2 cups). Finely grate 2 ounces Pecorino Romano or Parmesan cheese on the small holes of the grater (about 1 cup). Place both cheeses in a medium bowl and toss to combine. Coarsely chop 5 ounces baby spinach. Thinly slice 2 medium shallots (about 1 cup). Pick the leaves from 3 medium bunches fresh tarragon and coarsely chop until you have 2 tablespoons; chop more for garnish if desired. Drain 1 (14.5-ounce) jar or can quartered, marinated artichoke hearts.

Step 3

Gently crush 1 teaspoon coriander seeds with the bottom of a pan and place in a small bowl. Add 1 tablespoon za’atar and 1 teaspoon Aleppo or red pepper flakes.

Step 4

Heat 1 tablespoon olive oil in a 12-inch cast iron or broiler-safe skillet over medium-low heat until shimmering. Add the shallots and 1/2 teaspoon kosher salt, and cook until softened, about 4 minutes.

Step 5

Increase the heat to medium-high. Add the spinach and cook until the spinach is wilted and no liquid remains, 2 to 4 minutes. Add the artichokes and cook until warmed through, about 1 minute. Add 8 ounces mascarpone cheese and cook, stirring until fully melted into the spinach mixture. Add 1 cup half-and-half, stir to combine, and simmer for 2 minutes.

Step 6

Turn off the heat. Add the tarragon and 2 cups of the cheese mixture, and stir until combined. Taste and season with more kosher salt and freshly ground black pepper as needed.

Step 7

Transfer the skillet to the oven. Broil until bubbling all over, about 3 minutes. Remove the skillet from the oven. Use a spoon to gently push aside some of the spinach mixture to create a little well, then crack 1 large egg into the well. Repeat until you have cracked 8 large eggs total into the skillet. Sprinkle with the remaining cheese mixture.

Step 8

Return the skillet to the oven and broil for 4 minutes for runny yolks, or 6 minutes for medium yolks. Meanwhile, make the sauce. Melt 3 tablespoons unsalted butter into a small saucepan over medium-high heat. Continue to cook until the milk solids begin to brown and butter smells nutty, about 3 minutes. Turn off the heat and while vigorously whisking, add the spice mixture.

Step 9

To serve, drizzle the za’atar butter sauce all over the baked eggs and sprinkle with a pinch of flaky salt. Serve immediately with bread, rice, or potatoes.