Heat olive oil in a medium skillet over medium heat. Cook potatoes in hot oil, stirring occasionally, until tender but firm, about 10 minutes.
Mix in spinach, green onions, and garlic. Season with salt and pepper. Cook and stir until spinach is wilted, 1 to 2 minutes.
Beat together eggs and milk in a medium bowl. Pour over vegetables in the skillet. Sprinkle with Cheddar cheese. Reduce heat to low, cover, and cook until eggs are firm, 5 to 7 minutes.