Sauté the onion and garlic. Heat a non-stick frying pan over medium heat and melt the butter. Add the onion and garlic and cook, stirring frequently, until softened but not discoloured.
Add spinach to the pan. Place the spinach leaves on the onion and fry, stirring, for 5-6 minutes until the liquid that has formed on the bottom has completely evaporated. Then add half of the salt and pepper.
Crack the eggs. Make 4 wells in the spinach and crack the eggs into them. Season with salt and pepper. Cover the pan with a lid for 2-3 minutes to set the whites. Remove the pan from the heat and divide the omelette with spinach into plates.