Heat oven to 450ºF (232ºC) with racks set in upper-middle and lower-middle positions.
Toss onion with 2 tablespoon oil and ½ teaspoon salt on a sheet pan. Place garlic halves, cut side down, on sheet pan. Transfer to upper-middle rack of oven.
On a second sheet pan, toss tomatoes with 2 tablespoons oil and ½ teaspoon salt. Transfer to lower-middle rack of oven. Roast onions and tomatoes for 15 minutes then rotate sheets and continue roasting until vegetables are softened and starting to brown, about 15 more minutes.
Remove sheets from oven and let cool slightly. Once garlic is cool enough to handle, squeeze roasted cloves out of skins into blender. Scrape onions, tomatoes and their juices into blender along with 2 cups broth, oregano, paprika, and pepper flakes; blend until smooth.
Transfer to a pot and bring to a simmer over medium-low heat. Stir in cream and season to taste with salt and pepper. Serve with grilled cheese, buttery toasted bread, or croutons.