Scrub the mussels under cold, running water and remove the beards (pull towards the back of the mussel).

If any are open, tap them sharply, and if they close, they are fine. If they do not close, discard them. 

Place two tablespoonfuls of oil in a sauté pan over high heat. Add the mussels, cover, then cook for about 4 to 5 minutes. 

While they cook, shake the pan from time to time until the mussels open.

Remove the mussels with a slotted spoon and place in a bowl (discard any that did not open). Reserve a few mussels in their shells for serving, and remove the rest from their shells. Use an empty shell like tongs to pluck the mussels out. Set aside both bowls of mussels. 

Melt the butter and one tablespoon of extra virgin olive oil in a sauté pan over medium heat, then add the garlic, black olives, anchovy and parsley.

Increase the heat, then add the tomato sauce and two tablespoonfuls of water, salt and pepper.

Reduce the heat and simmer for 15 to 20 minutes. Meanwhile...

Add the pasta to salted water that is at a rolling boil.

Cook according to the directions on the package (to al dente). 

When the pasta is ready, toss the shelled mussels into the sauce. Taste the tomato base and add seasoning as needed.

Then add the pasta using a fork (don't drain the pasta, just take it from the water and place directly into the sauce). 

Toss the spaghetti and sauce gently and if too dry, add some of the pasta water. Place in a serving bowl to serve, or directly into dishes then add the reserved mussels in their shells on top.

Serve immediately.