Par-cook the potatoes: Add potatoes to a pot of salted water, bring to a boil, and cook until just fork-tender, about 8–10 minutes. Drain well. This step ensures soft centers without overcooking everything else.
Crisp the kielbasa: Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the sliced kielbasa in a single layer and cook 3–4 minutes per side until browned. Remove to a plate, leaving the drippings in the pan.
Sauté the veggies: Lower heat to medium. Add the remaining olive oil and the butter.
Stir in onions and peppers with a pinch of salt. Cook 5–7 minutes until soft and a little caramelized around the edges.
Add garlic and spices: Stir in garlic, smoked paprika, thyme, and red pepper flakes. Cook 30–60 seconds until fragrant.
Don’t let the garlic burn.
Build the sauce: Add tomato paste and Dijon, stirring to coat the veggies. Pour in broth, scraping up any browned bits. Simmer 2–3 minutes to thicken slightly.
Finish with potatoes and kielbasa: Return the kielbasa to the pan along with the drained potatoes.
Toss gently to coat everything in the sauce. Cook another 3–5 minutes so the flavors come together.
Brighten and season: Stir in the vinegar. Taste and season with salt and black pepper.
The acidity wakes up the smoky flavors.
Serve: Sprinkle with fresh parsley. Serve as is, or ladle over rice, buttered noodles, or a bed of sauerkraut for extra tang.