To to prepare the roasted garlic, cut the garlic tops off, sprinkle with 2 tablespoons of butter and 1/2 tsp each kosher salt and black pepper. Wrap in foil and bake at 375F for one our. Let cool, then squeeze the roasted garlic out of the skins into a small bowl. Mash with a fork and set aside.
In a large pot, melt the butter over medium-high heat. Add the olive oil as the butter is melting. Add the onions and the bell pepper, and season with salt and pepper. Cook until soft, constantly stirring. Add the minced garlic and cook for another minute. Add the flour, stir really well, then add the broth and mix. Stir in the tomatoes and the roasted garlic. Bring to a boil. Add the bay leaf. Drop the temperature to low, cover and let the soup simmer for 15 minutes.
Remove the bay leaf, stir in the cream, Parmigiano-Reggiano cheese and Tobasco sauce. Add the lemon juice, the remaining 2 Tbsp of butter and half of the chopped basil leaves.
Ladle the soup into bowls, sprinkle with the remaining chopped basil and serve.