Prepare croutons: Cut bread about 1 inch thick (cut horizontally for more surface area if using a baguette). Use a heart-shaped cookie or biscuit cutter and cut heart shapes from the slices.
Dry croutons: Let sit uncovered overnight or place on a baking sheet and place in the oven uncovered at 200 degrees Fahrenheit until dry.
Season croutons: Brush with olive oil (and smeared garlic if desired). Sprinkle with salt. Bake at 350 degrees Fahrenheit for about 5 minutes, turning over after 2-3 minutes, until light golden brown. Set aside.
Prepare tomatoes: Pour tomatoes and juice into a food mill. Pass through to separate seeds and skin from puréed liquid. Discard seeds and skin. Reserve strained liquid.
Sauté vegetables: In a pot, heat olive oil. Add garlic, shallot, and carrot and cook until softened.
Simmer soup: Add tomatoes and bouquet garni. Bring to a simmer and cook for 20-25 minutes.
Assemble and broil: Place soup in oven-safe bowls. Top with grated cheese and a drizzle of clarified butter. Broil until cheese is melted and bubbly.