3 1/2 cups beef or chicken stock
5 tbsp. unsalted butter
10 oz. Italian breadsticks
1 lb. Taleggio cheese, sliced
Kosher salt and freshly ground black pepper, to taste
1/2 small onion, thinly sliced
Bring stock to a boil in a saucepan; remove from heat. Grease bottom of a 3-qt. high-sided skillet with 1 tbsp. butter. Break breadsticks into 2 1/2″ pieces. Put 1 layer breadsticks in skillet. Cover breadsticks with layer of cheese. Continue layering breadsticks and cheese; ladle stock over breadsticks one ladleful at a time and heat skillet over low heat. Bring to a simmer; cook, without stirring, for 30 minutes.
Meanwhile, melt remaining butter in a 12″ skillet over medium heat. Add onions; cook, until onions are soft, 8?10 minutes. Set a fine sieve over a small bowl. Strain butter, pressing onions with back of a spoon; discard onions. Drizzle butter over soup; continue cooking for 10 more minutes. To serve, spoon onto serving plates.