Lay the tuna pieces out on a cutting board. Place one anchovy fillet, a pinch of fresh thyme and a fennel frond on each one and roll up to form an involtino. Secure each with two toothpicks.
Heat oil in a 12 to 14-inch pan over medium high heat until smoking. Cook the involtini two to three at a time until lightly browned and remove to a plate. Add onions, carrots, celery and bay leaves to pan and cook until softened, about 8 to 10 minutes. Add tomato sauce, vinegar and wine and bring to a boil. Lower heat and simmer 30 minutes until thick as porridge. Put tuna into sauce and simmer covered for 5 to 6 minutes, just to warm through. Remove toothpicks from involtini, add parsley and serve.