To prepare dressing: Mix the shallots, broth, oil, lemon juice, vinegar, mustard, basil, oregano, salt, black pepper, hot pepper sauce, and red pepper flakes in a 2-cup jar or bowl. Cover and shake or whisk (if using a bowl) until well mixed. Refrigerate until the salad is ready.
Bring two pots of water to a boil. In one, cook the green beans until crisp-tender, (5 minutes). In the other, cook the potatoes, covered, until tender, approximately 8-10 minutes. Drain the beans and potatoes and run under cold water until cooled. Transfer to a large bowl.
Add the tuna, onion, cucumber, tomatoes, and olives to the bowl. Drizzle the dressing evenly over the salad. Using your hands, gently toss the salad to coat. Refrigerate for 1 hour.
Before serving, bring to room temperature and serve over lettuce leaves garnished with the egg quarters.