Prep the vegetables and slice the sausages into rounds.
Heat olive oil in a large skillet over medium-high. Brown the bratwurst on both sides, then transfer to a plate.
Reduce heat to medium. Melt butter in the skillet, add onion and bell pepper, and cook until softened, about 4 minutes.
Stir in garlic, smoked paprika, and thyme. Cook 30 seconds until fragrant.
Add potatoes, salt, and pepper. Pour in the broth, cover, and steam until potatoes are just tender, 8–10 minutes.
Uncover and stir in Dijon and vinegar. Simmer to reduce slightly, 2–3 minutes.
Return the browned bratwurst to the pan. Toss and cook until the edges crisp and glaze forms, 3–5 minutes.
Finish with parsley. Taste and adjust seasoning, then serve hot.