Skewer each cabbage and yellow onion piece separately crosswise through the center with a slender wooden skewer (it pierces more easily than a thicker skewer). Cut skewers fairly short with kitchen scissors so they’ll fit in a stockpot.
Meanwhile, about 2 hours before you want to eat, bring 5 cups water and the lager to a boil in a 10- to 12-qt. stockpot. Toss in garlic, several sprigs of thyme, 1 sprig of rosemary, and the potatoes. Cover and increase heat to return pot to a boil.
Drop sausages, then yellow onions and cabbage into pot (it’s okay if cabbage isn’t completely submerged). Cover, return to a boil, and turn off heat. Let sit, covered, at least 30 minutes and up to 1 hour.
Heat a grill to medium-high (about 450°). When everyone is ready to eat, lift sausages and vegetables from pot, draining them. Grill in 2 batches, covered and turning once, until lightly browned, 7 to 10 minutes for vegetables and 5 to 7 minutes for sausages. As food is done, transfer to 2 large platters, remove skewers, and drape with foil to keep warm.
Grill green onions, turning once, to wilt lightly, 1 to 2 minutes total; arrange on the platters. Lightly sprinkle vegetables with chopped parsley and tuck in parsley sprigs. Serve with grainy mustard.