Heat oil and butter in a large pot over medium heat. Add leek and garlic. Cook, stirring often, until softened, 2 to 3 minutes. Stir in tomato paste. Cook, stirring, for 2 minutes. Add broth, tomatoes, bay leaves, oregano and salt. Bring to a boil, stirring occasionally. Reduce heat and simmer for 10 minutes.
Add tortellini. Simmer until the tortellini are tender, 4 to 7 minutes.
Remove the bay leaves. Whisk flour and half-and-half in a small bowl. Stir the mixture into the soup. Add basil (or parsley). Cook, stirring occasionally, until slightly thickened, about 1 minute.
