Bring broth, salt & butter to gentle simmer, add flour & stir until well combined then kill heat & keep mixing for a minute until you have a tight ball.
Place dough in mixer on low for a few minutes to cool then add eggs, one at a time.
Place dough in a plastic bag, cut corner off so you have a half inch hole, squeeze dough through hole & snip off with scissors into one inch logs & let them fall into simmering broth. Cook gently, covered for about 5 minutes.