Cheesy Rosti with Eggs

Name: Cheesy Rosti with Eggs
Ingredients: 500g baking potatoes, quartered, at room temperature; 1 tbsp sunflower oil; 1 small onion, peeled and finely chopped; 1 large garlic clove, or 2 small cloves, peeled and finely chopped; small bunch curly parsley, finely chopped; pinch grated nutmeg; salt and freshly ground black pepper; olive oil, to drizzle; 50g cheddar cheese, grated; sunflower oil; 2 medium free range eggs, at room temperature