In a large nonstick skillet with a lid, heat the oil over medium-high heat until shimmering. Add the potato, Brussels sprouts, mushrooms, and leek and toss to coat. Season to taste with salt and pepper. Cook, stirring occasionally, until the vegetables are tender, about 10 minutes.
Spread out the vegetable mixture to create four small wells. Crack an egg into each well. Season to taste with salt and pepper.
Cover and cook until the desired doneness is reached for the eggs, 5 to 8 minutes. Serve immediately.
Promptly store leftovers in an airtight container in the refrigerator, for up to 3 days.Nutritional values are approximate and based on 1/4 the recipe.