If desired, peel eggplant. Cut eggplant into 3/4-inch pieces (you should have about 3 cups).
In 3 1/2- or 4-quart slow cooker, combine eggplant, zucchini, yellow squash, cannellini beans, tomato, garlic, rosemary, pepper, and dried basil, if using. Add tomato juice.
Cover and cook on low-heat setting for 8 to 10 hours or on high-heat setting for 4 to 5 hours. Stir in fresh basil, if using, and balsamic vinegar.
Preheat oven to 400°F. Lightly brush bread slices with olive oil. Sprinkle with 1 tablespoon of the Romano cheese. Place bread slices on baking sheet. Bake for 6 to 8 minutes or until toasted.
To serve, ladle vegetable mixture into bowls. Top with croutons and sprinkle with remaining Romano cheese.