Heat a large sauté pan over medium heat. Once hot, add the guanciale and cook until fat is rendered and it’s golden brown. Remove with a slotted spoon and set aside, leaving fat in the pan.
Add diced onion and cook until golden, reducing heat if needed to prevent burning.
Add garlic and cook for 1 minute. Stir in tomato paste and cook until caramelized.
Add crushed tomatoes and anchovy. Simmer for 2 minutes, stirring occasionally.
Season with salt to taste. Add chopped basil and lemon zest.
Add mussels to the pan, cover with a lid, and cook for 3 minutes or until most mussels have opened. Discard any that remain closed. For best texture, remove mussels individually as they open.
Stir in the cooked guanciale. Divide into serving bowls and spoon sauce over the mussels. Serve immediately.