Motta Porrichu Spicy Coconut Ginger Omelette

Name: Motta Porrichu (Spicy Coconut Ginger Omelette)
Ingredients: 4 large eggs; 1/3 cup coconut cream (see Recipe Note); 1 small red onion , diced (about 1 1/2 cups ); 2 tablespoons grated fresh ginger; 2 tablespoons roughly chopped fresh curry leaves; 1 green bird's eye chili , finely chopped; 1 1/2 teaspoons pink salt or 1/2 teaspoon table salt; 1 1/2 teaspoons freshly ground black pepper; 1 1/2 tablespoons virgin coconut oil; Matta rice , for serving (optional)