Preheat the oven to 190c. Boil a large pan of water and cook the pasta for 1 minute less than recommended on the pack. Drain.
Whilst the pasta is cooking, heat the oil on a medium heat, in a large frying pan. Add the chicken, and cook until just sealed – about 5 minutes.
Add the onion and cook for a further 3-4 minutes until the onion is softened.
Add the chopped peppers, salt, pepper, garlic, tomato paste, oregano and thyme. Stir and cook for 2-3 minutes.
Stir in the tinned tomatoes and cream, bring to a gentle bubble, then add the pasta, spinach and cooked bacon. Stir everything together, then transfer to a large baking dish.
Top with the cheddar and mozzarella, and place in the oven for 20-25 minutes, until the cheese is golden brown.