• Set oven and prepare pan. Preheat the oven to 375°F and grease a 9 x 13 x 2-inch baking pan with 1 tablespoon of the olive oil.

Prepare the potatoes

• Use a food processor fitted with the blade attachment to grate the potatoes. Then use your hands to squeeze as much liquid as possible out of the potatoes, and add them to an extra large mixing bowl. (I usually do this about one handful at a time.) Combine with 2 of the eggs, the Parmesan, thyme, salt and a few grinds of black pepper.
• Add 2 tablespoons of the olive oil to a large sauté pan, place it over medium heat and add the potato mixture. Cook, stirring often, just enough to make the potatoes slightly tender, about 5 minutes. (Don't wash this pan - you'll need it again!)
• Add the sautéed potato mixture to the greased baking pan, and use your fingers or a small metal spatula to mold it along the bottom and sides.
• Place the pan in the preheated 375°F oven and bake until the potato crust is golden brown along the edges, about 35 minutes. (Keep the oven set to 375°F after you remove the pan.)

Make the spinach mixture

• While the crust is baking, coat the same large sauté pan you used for the potatoes with the remaining tablespoon of olive oil and place it over medium heat. Add the onion and garlic and cook until the onions are soft, about 7 minutes. Then add the spinach, in at least 4 batches, cooking each until it's wilted before adding the next. Once all of the spinach has wilted, cook off any remaining liquid that's in the pan. Season to taste with salt and pepper. (Here's How to Season to Taste.) Turn off the heat and let it cool for a few minutes. Then add the grated Cheddar and mix it in quickly as it will begin to melt a bit. Set aside.

Assemble and bake

• When the crust is done, add an even layer of the thinly sliced prosciutto directly on top. Follow this with the spinach mixture, spreading it out evenly. Then use a spoon to make 9 evenly spaced shallow indentations, and crack an egg into each one.
• Bake in the preheated 375°F oven just until the eggs are cooked, about 25 minutes.
• Let it rest for about 10 minutes before serving.