Clean and beard the mussels. Place a large spaghetti pot over medium heat, add the oil and onions, and cook for 2 minutes until sizzling. Add the mussels and the wine to the pot, cover, and cook until the mussels have all steamed open, about 6-8 minutes. Remove the mussels with a spoon or spider and leave the liquid and onions in the pot. Allow the mussels to cool and remove them from their shells and set the mussels aside. Discard the shells.
Meanwhile, cook the mussel liquid until only a little moisture remains, about 3-4 tablespoons. Add the peppers, thyme leaves, chili flakes, and garlic, and cook over medium heat until softened, about 8-10 minutes. Add the tomato paste and mix well. Cook for 5 more minutes, stirring often. Remove the mixture from the heat and allow to cool.
Combine the pepper mixture with the shucked mussels, the remaining oil, and the orange segments and juice. Refrigerate until ready to serve.
Toast the 4 slices of bread and rub each with the remaining garlic. Spoon the mussel mixture over the bread, lay a couple of basil leaves over each and serve with a small, bitter salad.