Slice the smoked Polish sausage into ½-inch rounds.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the sausage slices and cook, stirring occasionally, until browned and crispy, about 5–7 minutes.
Transfer the browned sausage to a plate and set aside.
If needed, add the second tablespoon of olive oil to the same skillet.
Add the chopped onion, chopped bell peppers, and potato pieces.
Cook, stirring occasionally, until the onion is softened and potatoes begin to brown, about 10–12 minutes.
Stir in the minced garlic, smoked paprika, dried thyme, salt, and black pepper and cook until fragrant, about 1 minute.
Pour in the chicken broth, scraping up any browned bits from the pan, and bring to a simmer.
Return the sausage to the skillet, stir to combine, then reduce heat to medium-low and cover.
Simmer until potatoes are fork-tender, about 15–20 minutes.
If the mixture is too liquidy, uncover and cook a few minutes more to reduce.
Taste and adjust seasoning before serving.