Brown the sausage. Heat the vegetable oil in a large, deep skillet or Dutch oven over medium heat. Add the sausage and cook for 5–7 minutes, turning until browned on both sides. Transfer to a plate. Leave about 1 tablespoon of fat in the pan, removing any excess.
Cook the vegetables. Add the butter, onion, carrot, and red bell pepper. Cook for 7–8 minutes, stirring occasionally, until the vegetables begin to soften.
Add the tomato paste and seasonings. Stir in the tomato paste and cook for 1 minute. Add the garlic, sweet paprika, thyme, salt, and black pepper. Cook, stirring, for about 30 seconds.
Add the broth and potatoes.
Add the broth and potatoes. Pour in the chicken broth, scraping up any browned bits from the bottom of the pan. Add the potatoes and bay leaves, then bring to a gentle simmer.
Simmer until tender. Cover, reduce the heat to low, and simmer for about 30 minutes, stirring occasionally. Check that the potatoes are easily pierced with a fork. If they are still firm, cook for another 5 minutes or until tender.
Thicken the stew. Mash a few potato pieces directly in the pan, leaving most of them whole. Stir to combine, then return the sausage and any juices from the plate.
Finish cooking. Simmer uncovered for another 5–7 minutes, stirring occasionally, until the sausage is hot and the sauce has thickened. Add a splash of broth if the stew becomes too thick.
Add parsley and rest. Remove the bay leaves and stir in the parsley. Taste and adjust the seasoning if needed. Let the stew rest off the heat for 5 minutes before serving.