Combine 1 can of white kidney beans and 2 cups broth in a blender. Blend to a smooth puree and pour into a large saucepan. Add remaining beans, remaining broth, tomatoes, onion, garlic, basil, thyme, and black pepper. Bring soup to a boil over medium-high heat, about 5 minutes. Reduce heat to a simmer, cover, and cook until beans are tender, 10 to 15 minutes.
