In a large pot, heat the olive oil over medium heat. Add the onion, carrots, and celery. Cook for 5-7 minutes, stirring occasionally, until the vegetables are softened.
Add the garlic and cook for 1 minute more, until fragrant.
Pour in the broth and diced tomatoes. Add the bay leaf and thyme. Season with salt and pepper.
Bring the soup to a boil, then reduce heat and simmer for 10 minutes.
Add the pastina and continue simmering for 8-10 minutes, until the pasta is tender.
Remove the bay leaf and thyme sprigs. Taste and adjust seasoning as needed.
Ladle the soup into bowls and garnish with freshly grated Parmesan cheese.