In a medium bowl, whisk the eggs, Parmesan cheese, parsley, ½ teaspoon of salt, ⅛ teaspoon of pepper, and the cayenne. Heat 2 tablespoons of olive oil in a 10-inch ovenproof nonstick skillet over medium-high heat. Add the diced potato and ¼ teaspoon of salt and cook, stirring occasionally, until browned, 6 to 7 minutes. Transfer the potato to a bowl. Reduce the heat to medium. If the pan is dry, add the remaining 1 tablespoon of olive oil. Add the onion and cook, stirring frequently, until it softens and begins to brown, 4 to 5 minutes. Stir in the asparagus, garlic, the remaining ¼ teaspoon of salt, and ⅙ teaspoon of pepper. Cook, stirring frequently, until the asparagus is bright green and crisp-tender, 3 to 4 minutes. Lower the heat to medium-low and add the egg mixture and potatoes, stirring until the ingredients are combined, 10 to 15 seconds. Add the cheddar and stir until mixed in. Cook without stirring until eggs have almost set, 10 to 12 minutes. Meanwhile, position an oven rack 6 inches from the broiler element and heat the broiler to high. Transfer the skillet to the oven and broil until the eggs have set completely and the top of the frittata is golden brown, 1 to 3 minutes. Let rest for 5 minutes. Gently transfer to a cutting board, slice into 4 wedges and serve.
