Combine butter and olive oil in a Dutch oven over medium heat; add sausages and cook until browned on all sides, 6 to 8 minutes.
Stir onion, pinch of salt, and pinch of pepper in with the sausages. Cook and stir until onions are slightly translucent and caramelized, about 5 minutes.
Stir garlic into sausage mixture; cook and stir for 30 seconds.
Pour apple cider into sausage mixture; increase heat to medium-high and stir in potatoes. Bring to a simmer.
Pour cabbage over top of sausage mixture and reduce heat to medium-low. Cover and simmer until potatoes are tender, 20 to 25 minutes. Remove sausages and potatoes from the Dutch oven and set aside.
Increase heat to high, simmer liquid until thick and reduced by half, about 5 minutes.
Return potatoes and sausages to the Dutch oven and remove from heat. Season with salt and pepper to taste. Garnish with mustard and parsley.
1 1/2 teaspoons butter1 teaspoon olive oil4 links chicken and apple sausage1 onion, sliced1 pinch salt and freshly ground black pepper to taste3 cloves garlic, crushed3 cups apple cider or apple juice1 pound small Yukon Gold potatoes, scrubbed but not peeled1 1/2 pounds finely shredded green cabbagesalt and freshly ground black pepper to taste2 tablespoons Dijon mustard, for garnish2 tablespoons chopped fresh parsley, for garnish