This recipe is bursting with fresh flavors and it's everything you love about breakfast food in one 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.
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 it's golden brown along the edges, about 25 minutes. (Keep the oven set to 375°F after you remove the pan.)
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 two batches, cooking it just until it's wilted. Mix in the Gruyère and season generously to taste with salt and pepper. (Here's How to Season to Taste.) Set aside.
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.