Wash the mussels and remove any beards using a small knife. Rest them in cold water for 10 minutes or so to remove any grit.
Meanwhile, make the sauce. Finely chop the onion, celery and garlic. Dice the carrots.
Heat 1 Tbsp olive oil in a large, shallow pan, then add the onion & celery and gently sauté for 5 minutes. Add the garlic and chilli, then cook for 3 more minutes, until the veggies are tender. Add the wine, stir for a minute, then add the tomato purée and tinned tomatoes. Season with salt &pepper. Bring to the boil, then gently simmer for 15 minutes.
While the sauce is cooking, bring a pan of lightly salted water to the boil and cook the spaghetti for about 10 minutes, following the packet instructions. When it’s cooked (it should be al dente), drain and keep it warm in the pan, under cover.
Drain the mussels and add them to the tomato sauce. Cover the pan and bring to the boil. Simmer until the mussels have opened – it should take about 5 minutes. Discard any that haven't opened.
Add the drained spaghetti and gently toss everything together.
Serve immediately, with chopped parsley scattered on top.