Preheat oven to 350°F.

In large ovenproof skillet heat oil. Cook onion and garlic until translucent.

Add Brussels sprouts, mushrooms, sweet potato and salt. Cook covered, stirring occasionally, until sprouts and mushrooms soften.

Stir in ham. Use spoon to form four evenly spaced wells in mixture. Crack an egg in each well. Sprinkle cheese on top.

Bake in oven 10-15 minutes, until egg white cooks.