Heat olive oil in a large pot over medium heat. Add the diced onion, celery, and carrots. Sauté for about 5 minutes until the vegetables are softened.
Stir in garlic, tomato paste, Italian seasoning, dried thyme, salt, and black pepper. Cook for 1 minute until the mixture is fragrant.
Add the diced tomatoes, low-sodium vegetable broth, frozen corn and peas, and bay leaf. Bring the mixture to a boil. Then add dry alphabet pasta and reduce the heat to let it simmer for 8 to 10 minutes, or until the pasta is cooked but still firm.
Remove the bay leaf and taste the soup. Adjust salt, pepper, and Italian seasoning if needed.
Garnish with fresh chopped parsley and Parmesan if desired, and serve with a side of crusty bread.