Preheat oven to 425°F. Divide tomatoes, onions + garlic between 2 sheet pans. Drizzle with olive oil and season generously with salt, pepper, oregano + red pepper flakes.
Roast 45–60 min, rotating halfway through, until tomatoes are collapsed and edges are caramelized.
Melt 1 tbsp butter in a large pot over medium heat. Add tomato paste + rosemary and cook 2–3 min, until paste darkens.
Add roasted veggies + ALL the juices from the pans. Add broth* and basil. Simmer uncovered for 10–15 min.
Blend until smooth. Add more broth/water if needed.
Reduce heat to low and stir in heavy cream + remaining 1 tbsp butter. Season to taste.
Serve with sourdough grilled cheese, obviously.
