1. Place 1 tablespoon canola oil, 1 egg, and beans in a food processor. Pulse 20 times or until mixture becomes a coarsely chopped paste. Combine bean mixture, 5 tablespoons panko, onions, and next 5 ingredients in a bowl.
2. Place 3 tablespoons panko in a dish. Divide bean mixture into 4 equal portions. Shape each into a 3/4-inch-thick patty; dredge in panko. Heat a nonstick skillet over medium-high heat. Add 4 teaspoons canola oil. Add patties; cook 3 minutes on each side. Remove from pan. Wipe pan clean. Add remaining 2 teaspoons canola oil. Crack 4 eggs into skillet. Cover and cook 4 minutes. Remove from heat.
3. To prepare salad, combine olive oil and next 4 ingredients in a bowl, stirring with a whisk. Add lettuce; toss gently to coat. Arrange 1 1/2 cups salad, 1 black bean patty, and 1 egg on each of 4 plates. Serve immediately.