Heat olive oil in a 4- to 6-quart Dutch oven over medium heat. Add diced onion and carrots and sauté until softened and slightly golden, about 6–8 minutes.

Stir in garlic and cook 30–45 seconds until fragrant, then add tomato paste and cook 1 minute.

Pour in crushed tomatoes, chicken broth, and add chopped sun-dried tomatoes or extra tomato paste. Stir to combine.

Add dried oregano, dried basil, crushed red pepper (if using), bay leaf, salt, and pepper. Bring to a gentle simmer and cook, partially covered, for 12–15 minutes. Remove and discard the bay leaf.

Optional: Use an immersion blender to smooth the soup or carefully transfer half to a blender and puree, then return to the pot.

While the soup simmers, bring a large pot of salted water to a boil. Cook the cheese tortellini according to package directions minus 1 minute (slightly undercooked). Reserve 1/2 cup pasta cooking water, then drain tortellini.

Stir half-and-half and chopped parsley into the hot soup off a vigorous boil; taste and adjust seasoning. Add drained tortellini and gently fold to combine, using up to 1/4 cup reserved pasta water to loosen the broth if needed. Heat through for 1–2 minutes and serve with grated Parmesan.