Top this soup with a dollop of our homemade pesto, which you can make in a mini food processor or blender. In a hurry? Store-bought pesto makes an excellent stand-in—although it’s not as light as our version.
Heat 5- to 6-quart Dutch oven over medium-high heat until hot.
Add barley and cook until toasted and fragrant, 3 to 4 minutes, stirring constantly.
Transfer barley to small bowl; set aside.
Add oil to same Dutch oven.
When hot, add cabbage, carrots, celery, and onion; cook until tender and lightly browned, 8 to 10 minutes, stirring occasionally.
Add garlic and cook until fragrant, 30 seconds.
Stir in barley, water, broth, tomatoes with their juice, and salt.
Cover and heat to boiling over high heat.
Turn heat to low and simmer 25 minutes.
Stir zucchini and beans into pot; increase heat to medium, cover, and cook until vegetables are barely tender, 10 to 15 minutes longer.
Meanwhile, prepare pesto: In blender container with narrow base or in mini food processor, combine basil, oil, water, and salt; cover and blend until mixture is pureed.
Transfer pesto to small bowl; stir in Romano and garlic.