Bring a large pot of salted water to boil. Bring 1 TBSP butter to room temperature. Wash and dry all produce. Peel and halve carrot lengthwise; thinly slice crosswise. Halve, peel, and dice onion. Trim, then thinly slice scallions, separating whites from greens. Mince 1 clove garlic. Drain beans.

Heat a large drizzle of olive oil in another large pot over medium-high heat. Add carrot and onion. Cook, stirring, until slightly softened, 4-6 minutes. Add another large drizzle of olive oil. Stir in scallion whites, minced garlic, Italian seasoning, and celery salt. Cook until fragrant, 1-2 minutes.

Once water is boiling, add half the pasta to pot (use remaining pasta as you like). Cook until just shy of al dente, 9-11 minutes. Reserve 1 cup pasta cooking water, then drain well and set aside.

Meanwhile, adjust rack to top position and preheat broiler to high. (TIP: If you have a toaster oven, use it instead!) Add tomatoes, stock concentrates, and 2 cups water to pot with vegetables. Bring to a boil, then reduce heat to a simmer. Stir in beans and simmer until vegetables and beans are tender, 8-10 minutes. Stir in pasta and reserved pasta cooking water. Simmer until pasta is al dente, 2-3 minutes. Season with salt and pepper.

Halve remaining garlic clove. Halve ciabatta (as if you were making a sandwich). Place on a baking sheet or piece of foil and toast under broiler (or in toaster oven) until golden brown and crisp, 2-3 minutes. Rub with cut sides of garlic, then spread with softened butter, sprinkle with half the Parmesan, and season with salt and pepper. Return to oven and broil until cheese has melted, about 1 minute. Halve each piece diagonally.

Stir 1 TBSP butter into soup until melted. Taste and season with salt and pepper. Divide soup between bowls. Sprinkle with scallion greens and remaining Parmesan. Serve with garlic bread for dipping.