Mushroom Omelette

Name: Mushroom Omelette
Ingredients: 1⁄2 lb. sliced mixed fresh mushrooms, such as criminis and wild chanterelles; 1 large yellow onion, peeled and sliced; 1 tsp. sugar; 1⁄4 cup extra-virgin olive oil; 3 scallions, trimmed and chopped into 1 pieces; 2 cloves garlic, peeled and minced; 1 tbsp. red-wine vinegar; 8 eggs; Salt and freshly ground black pepper; Leaves from 4-5 sprigs flat-leaf parsley, chopped