Clean, gut and wash the mullet. Heat oil in a pan over medium heat, add finely chopped onion and peeled, crushed garlic and sauté until golden. Discard the garlic and stir in crumbled thyme and bay leaf.
Combine well, add tomato purée and season with salt and pepper. Bring to a boil and cook over low heat for 15 minutes. Add parsley and mullet, seasoned with salt and pepper, and cook for 5 - 10 minutes, depending on size. Arrange mullet on a serving platter, garnish with chopped parsley and serve.