Heat the olive oil in a large pot over medium heat. Add the onion and cook for 3 minutes until it softens. Stir in 3 of the minced garlic cloves and cook for 1 minute more.
Pour in the crushed tomatoes and vegetable broth. Bring the mixture to a simmer and cook for 10 minutes. Reduce the heat to low and stir in the heavy cream, fresh basil, salt, and black pepper. Add the tortellini and simmer for 5 minutes until the pasta is tender.
While the soup simmers, slice the baguette in half lengthwise. Mix the softened butter with the remaining 2 minced garlic cloves, parsley, and Parmesan cheese. Spread the mixture over the cut sides of the bread. Place the bread on a baking sheet and broil for 2 to 3 minutes until the edges turn golden.
Ladle the soup into bowls and serve with pieces of the warm garlic bread on the side.