In a large skillet, heat olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until softened. Add the minced garlic and cook for an additional minute until fragrant.
Transfer the sautéed onion and garlic to the slow cooker. Add the diced carrots, celery, zucchini, green beans, diced tomatoes, vegetable broth, kidney beans, oregano, basil, salt, and pepper. Stir to combine.
Cover and cook on low for 6-8 hours or on high for 3-4 hours, until the vegetables are tender.
About 30 minutes before serving, stir in the pasta and fresh spinach. Cover and continue cooking until the pasta is al dente.
Taste and adjust seasoning if necessary. Serve hot, garnished with grated Parmesan cheese if desired.