Heat olive oil over medium-high heat in a 12” oven-proof skillet. Place potatoes in the pan, cover and cook 10 minutes until tender but firm.
Add spinach, green onions and garlic to the pan along with a pinch of salt and pepper to taste. Cook until spinach wilts, stirring occasionally, about 2-3 minutes.
In a medium bowl whisk together eggs. Pour into the skillet over the vegetables. Stir once then sprinkle with Parmesan cheese. Reduce heat to low, then cover and cook until eggs are firm, about 5-7 minutes.
Place skillet in the oven under the broiler and heat until eggs are cooked through, about 3 minutes, checking carefully so they don’t burn.
Turn onto a plate. Garnish with parsley.
Serve warm, room temperature or chilled.