In a medium skillet, heat the EVOO, 3 turns of the pan, over medium-low heat until hot. Add the anchovies and cook until melted, 2 minutes. Add the potatoes, parsley, garlic and crushed red pepper; spread evenly in the pan and season with black pepper. Cook, turning, until the potatoes are golden, about 10 minutes. Fold in the dandelion greens, season with nutmeg and cook over low heat, turning a few times, until softened, 7 to 8 minutes.
In a large nonstick skillet, melt 1 tablespoon butter over medium-low heat. Crack in 4 eggs, season with black pepper, flip and cook to desired doneness, 3 to 7 minutes. Repeat with the remaining 1 tablespoon butter and 4 eggs. Serve with the potatoes and greens.