One bowl of this hearty soup provides three of the recommended five daily servings of vegetables.
Cover beans with 6 cups cold water in a large pot. Bring to a boil; remove from heat. Let stand, covered, 1 hour.
Drain beans; return to pot. Cover with 3 quarts cold water. Add bay leaf and thyme; bring to boil. Reduce heat to medium; simmer, partially covered, until beans are barely tender, about 2 hours.
Add leeks, carrots, potatoes, tomatoes, broth, and 2 cups water. Simmer, partially covered, until the beans are tender, about 30 minutes to 1 hour.
Make pesto: Finely chop garlic in a food processor. Add basil; process. Add cheese and oil; process until combined.
Add green beans and zucchini to pot. Cook, uncovered, 20 minutes. Add peas; cook until soft, 5 to 10 minutes. Season with salt and pepper. Divide among bowls; top each with 1 heaping teaspoon pesto.