1. COOK BEANS Bring beans and enough water to cover by 1 inch to low boil in medium saucepan over high heat. Reduce heat to low and simmer, covered, until beans are just beginning to soften, about 20 minutes. Drain beans and transfer to slow cooker.
2. SAUTÉ AROMATICS Heat 3 tablespoons oil in Dutch oven over medium heat until shimmering. Add onions and carrots and cook until softened, about 5 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Add tomatoes and cook until pan is nearly dry, 5 to 7 minutes. Stir in broth, water, 1⁄2 cup basil, oregano, and pepper flakes and bring to boil; transfer to slow cooker. Cover and cook on low until beans are tender, 6 to 7 hours (or cook on high 5 to 6 hours).
3. FINISH SOUP Stir zucchini, chard, and pasta into slow cooker and cook, covered, on high until pasta is tender, 20 to 30 minutes. Stir in remaining basil and remaining oil. Season with salt and pepper. Serve.
MAKE AHEAD: Soup can be made through step 2 and refrigerated in airtight container for 2 days. To finish, bring to boil in Dutch oven. Stir in zucchini, chard, and pasta; reduce heat to low; and simmer until pasta is tender, about 10 minutes.