Heat olive oil in a large skillet over medium heat. Add diced onion, carrots, and celery. Cook, stirring occasionally, until vegetables are softened, about 5 minutes.
Add minced garlic to the skillet and cook for 1 minute until fragrant. Remove from heat.
Transfer the sautéed vegetables and garlic to the slow cooker.
Pour in the chicken broth and water. Stir in dried oregano, dried basil, dried thyme, crushed red pepper flakes, black pepper, and salt.
Add the frozen meatballs to the slow cooker and stir to combine.
Cover and cook on low for 3 hours.
After 3 hours, add the small pasta to the slow cooker. Stir well.
Cover and cook on low for an additional 30 to 45 minutes, or until the pasta is tender.
Stir in the chopped baby spinach and grated Parmesan cheese. Cook uncovered for 5 minutes until the spinach wilts.
Taste and adjust seasoning with additional salt and pepper if needed.
Ladle soup into bowls and garnish with extra grated Parmesan cheese before serving.