Add the olive oil and butter to a large soup pot over medium heat, followed by the onion and garlic. Cook, stirring occasionally for about 5 minutes. Add the tomatoes and tomato paste, stir, and let them cook for another 5-7 minutes.
Stir in the salt, pepper, and vegetable broth. Bring to a boil then lower heat to medium-low and cook, uncovered, for 10 minutes to steam off some of the tomato juices.
Use an immersion blender to puree the soup, or carefully transfer it in batches to a blender and blend until smooth. Add the tortellini to the soup, increase the heat to medium, and cook for another 7-8 minutes, or until the tortellini is tender but not falling apart.
Stir in the Greek yogurt, taste, and adjust seasonings as desired. Ladle into bowls and enjoy warm, perhaps topped with fresh basil and a side of crunchy bread.