Preheat oven to 200C. Cook the pasta in a large saucepan of boiling water following packet directions or until al dente. Drain well.
Meanwhile, heat oil in a large frying pan over medium heat. Add onion, carrot and celery and cook, stirring, for 5 mins or until onion softens. Add mince and cook, stirring with a wooden spoon to break up any lumps for 5 mins or until mince changes colour and is cooked through. Add the tomato pasta sauce and thyme and cook for a further 5 mins or until sauce thickens slightly. Add the spinach and gently stir to combine.
Add the cooked pasta to the sauce and stir to combine. Season. Spoon pasta mixture evenly among four 2-cup (500ml) ovenproof dishes. Place on a baking tray. Sprinkle each dish evenly with cheddar and top with a sprig of thyme. Bake for 15-20 mins or until heated through and cheddar is golden brown. Serve immediately with lettuce leaves.