Warm a large skillet over medium heat. Brown the kielbasa rounds until lightly crisp, 4–6 minutes. Drain excess fat.
Whisk the cider, apple jelly, brown sugar, Dijon, vinegar, garlic, red pepper flakes, salt, and pepper in a bowl.
Pour the glaze into the skillet. Simmer, stirring often, until the sauce reduces slightly, 6–8 minutes.
Stir cornstarch with water. Drizzle into the pan and cook until the glaze turns glossy and clings, 1–2 minutes.
Stir in butter to finish. Sprinkle with parsley and serve warm with picks.