Preheat oven to 425°. Crush tomatoes with your hands into a 13×9″ baking dish; scatter garlic over and drizzle with 1/4 cup oil; season with salt and pepper. Roast, tossing halfway through, until garlic is very soft and tomatoes are jammy, 35–40 minutes. Using a potato masher or fork, mash to break up garlic and tomatoes.

Heat 2 Tbsp. oil in a large heavy pot over medium-high. Add onion and season with salt and pepper. Cook, stirring occasionally, until onion begins to soften, about 5 minutes. Reduce heat to medium-low, cover pot, and cook, checking and stirring occasionally, until onion is very soft, 25–30 minutes (this long, slow cooking draws out maximum flavor). Increase heat to medium-high, add tomato paste, and cook, stirring, until slightly darkened in color, about 2 minutes. Add roasted tomato mixture and broth and bring to a boil. Reduce heat and simmer, stirring occasionally, until flavors meld, 15–20 minutes. Let cool slightly.

Meanwhile, strip leaves from rosemary sprig and toss with bread and remaining 2 Tbsp. oil on a clean rimmed baking sheet; season with salt and pepper. Toast, tossing once, until croutons are golden brown, 6–8 minutes.

Working in batches, purée tomato mixture in a blender until very smooth (make sure lid is slightly ajar to let steam escape; cover with a towel). Transfer to a large bowl or pitcher.

Pour soup back into pot. Taste and season with salt and pepper; keep warm.

Serve soup topped with butter and rosemary croutons.

Do ahead: Tomato soup and croutons can be made 4 days ahead. Let soup cool; cover and chill. Store croutons airtight at room temperature.