1. Pour tomatoes and puree into a bowl, then break up into small pieces with a wooden spoon or kitchen shears; set aside. Melt butter in a 6-qt pot over medium heat. Add the onion, scallions, and garlic. Cook, stirring occasionally, until the onions are just soft, 3 to 5 min. Add the tomato paste and flour and stir about 1 min to cook the flour and heat through. Stir in broth, milk, artichokes, salt, and tomatoes in puree.
2. Bring soup to a simmer but do not boil. Cover pot and simmer, stirring occasionally, until onions are soft and flavors have blended, 15 to 20 min.
3. Add cheese and cream, stirring until cheese is melted. Serve soup topped with extra sliced scallions if desired. The soup can be refrigerated for up to 5 days. Soup will thicken when chilled; thin with milk or broth. Do not freeze.