Prepare Vegetables and Ham: Start by chopping the onion, bell pepper, and mushrooms. Grate the carrot and mince the garlic. Dice the ham into small cubes.
Heat Oil in the Pan: In a large frying pan, heat a small amount of vegetable oil over medium heat. Once heated, add the onion and garlic, cooking until softened and fragrant.
Sauté Vegetables: Add the diced bell pepper, grated carrot, and chopped mushrooms to the pan. Sauté the mixture for about 5–7 minutes, until the vegetables are tender and the flavors have melded together.
Prepare the Egg Mixture: In a bowl, whisk the eggs with milk, salt, paprika, black pepper, and flour until well combined. Stir in the shredded cheese for added creaminess and flavor.
Add the Ham: Stir the diced ham into the vegetable mixture and let it cook for an additional 2–3 minutes, allowing the ham to warm through and release its savory flavors.
Combine Egg Mixture: Pour the egg mixture over the sautéed vegetables and ham, ensuring it is spread evenly. Reduce the heat to low, cover, and cook for about 10–15 minutes, or until the eggs are set and cooked through.
Serve: Once cooked, remove the dish from the heat and let it rest for a few minutes. Garnish with freshly chopped green onions, then slice and serve warm.