In a large sauté pan or sauce pot big enough to accommodate the mussels, sauté onion, peppers, chorizo, garlic and rosemary sprig in olive oil for about 5 minutes on medium-low heat, until onion is soft and translucent.
Prior to cooking the mussels, press together the shells of any mussels that are open. If the shell doesn't close, the mussel should be discarded (also toss any with broken shells). Add mussels and wine to the pan or sauce pot, mixing with the other ingredients. Cover and cook on high heat for about 5 minutes, or until the mussels have just opened. Discard any mussels that do not open.
Transfer mussels and their broth to individual serving bowls. Garnish with parsley and serve with crusty bread for sopping up the juices.