Spread the bread crumbs on a baking sheet and toast until lightly golden and crisp, about 5 minutes. Pulse the bread in a food processor until coarse bread crumbs form. Strain the clam juice through a cheesecloth-lined sieve and reserve 3 tablespoons.
Working over a bowl to catch the juices, remove and discard the top shells of the clams. Strain the liquid and reserve for another use. Add the clams, cover and steam over high heat until the clams open, 5 to 7 minutes transfer the clams to a baking sheet to cool. In a large saucepan, combine the wine, celery, onion and carrot and bring to a boil.