Cover the beans with water to a depth of 1 inch (2.5 cm) and allow to soak 4 hours or overnight. Drain the beans, place them in a saucepan, and cover with water to a depth of 1 inch (2.5 cm). Add the carrot, onion, celery, garlic, and bunch of herbs. Bring to a simmer and cook, partly covered, until the beans are tender, about 45 minutes to 1 hour.
In the beginning of the cooking, you may have to skim foam that collects on the surface. When the beans are tender, drain them, reserving about ½ cup (125 ml) of the cooking liquid.
Puree all but 1 cup (250 g) of the beans in a food processor with the cooked garlic, carrot, onion, and reserved cooking liquid. Add 2 tablespoons (30 ml) of the olive oil and season with salt and pepper.
Transfer to a saucepan and set aside.
Slice the scallops in half horizontally. Mix the bread crumbs with the cheese, parsley, and thyme and season with salt and pepper. Dust the scallops with the bread crumb mixture.
Heat the remaining oil in a heavy skillet. Lightly brown the slices of sea scallops in the oil, then transfer them to absorbent paper.
Toss the reserved cup of beans in the skillet just enough to reheat them. Reheat the bean sauce.
To serve, spoon 5 to 6 tablespoons (75 to 90 ml) of the bean sauce on each of 4 warm plates.
Arrange 5 slices of the scallops, slightly overlapping, in a circle on the sauce.
Spoon a few tablespoons of the whole beans in the center, garnish with sprigs of thyme and serve.
