Heat oil in a large saucepan over medium-high heat. Add shallots, carrot, chilies, garlic, and ¼ teaspoon each salt and pepper. Cook, stirring often, until vegetables are just tender, 6 to 8 minutes.
Add tomatoes and their juices along with the broth, bring to a boil, and then add farro and cook until tender, 20 to 25 minutes.
Stir in shrimp and chard, and cook until shrimp are opaque, 2 to 4 minutes. Transfer the soup to bowls and sprinkle with the basil and additional sliced chilies. Serve with the bread.
