Prep your ingredients: Slice the sausage into coins if using links, or remove casings if using bulk sausage. Core and slice the apples (leave the skin on for texture).
Thinly slice the onion.
Brown the sausage: Heat a large skillet over medium-high. Add olive oil if needed. Cook the sausage until browned and cooked through, 5–7 minutes.
Transfer to a plate, leaving drippings in the pan.
Soften the onions: Add butter if using, then the onions with a pinch of salt. Cook over medium heat, stirring occasionally, until golden and softened, 6–8 minutes. Don’t rush this—caramelized edges add depth.
Add apples: Stir in the apple slices and a small pinch of salt.
Cook 3–4 minutes, until they begin to soften but still hold shape. You want tender-crisp, not mushy.
Season: Sprinkle in thyme, cinnamon or allspice (if using), and red pepper flakes. Stir until fragrant, about 30 seconds.
Deglaze and balance: Add apple cider vinegar and Dijon.
Scrape up browned bits from the pan. If the skillet looks dry, stir in a splash of chicken broth.
Combine: Return the sausage and any juices to the skillet. Toss everything together and cook 1–2 minutes to marry the flavors.
Taste and adjust salt and pepper.
Serve: Spoon over grains or mashed potatoes, or pile into toasted buns with a smear of mustard. Garnish with extra thyme if you like.