STEP - 1
Preheat oven to 425°.
STEP - 2
Crush tomatoes with your hands into a 13x9" 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.
STEP - 3
Using a potato masher or fork, mash to break up garlic and tomatoes.
STEP - 4
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 boil. Reduce heat and simmer, stirring occasionally, until flavors meld, 15–20 minutes. Let cool slightly.
STEP - 5
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.
STEP - 6
Working in batches, purée tomato mixture in a blender until very smooth.Transfer to a large bowl or pitcher.
STEP - 7
Pour the soup back into pot. Taste and season with salt and pepper; keep warm.
STEP - 8
Serve soup topped with butter and rosemary croutons.