Brown the sausage: Heat the olive oil in your skillet over medium heat. Add the sausage links and cook until browned on all sides, about 8-10 minutes. They don't need to be fully cooked through yet. Transfer sausages to a plate.
Sauté the vegetables: In the same skillet with the sausage drippings, add the sliced onions and bell peppers. Cook until they begin to soften and caramelize, about 5-7 minutes. Add the garlic, dried oregano, and red pepper flakes (if using), and cook for another minute until fragrant.
Slice the sausage: While the vegetables cook, slice the sausages into 1/2-inch rounds. They'll still be a bit pink inside, and that's perfectly fine.
Add tomatoes and return sausage: Stir the drained diced tomatoes into the vegetable mixture. Return the sliced sausage to the skillet and stir to combine. Season with salt and pepper to taste. Let everything simmer together for about 5 minutes.
Transfer and keep warm: Transfer this sausage and pepper mixture to a bowl and cover to keep warm. Don't wash the skillet—those flavor bits are gold!
Make the polenta: In the same skillet, bring the chicken broth to a boil. Slowly whisk in the polenta in a steady stream, stirring constantly to prevent lumps. Reduce heat to low and cook, stirring frequently, for about 3-5 minutes until thickened (time will vary based on your polenta type, so check package instructions).
Finish the polenta: Once the polenta has thickened, remove from heat and stir in the Parmesan cheese and butter until melted and incorporated. Season with salt and pepper to taste.
Combine and serve: You have two options:
For family-style serving: Spread the polenta evenly in the skillet and top with the sausage and pepper mixture.
For restaurant-style plating: Spoon polenta onto individual plates and top with the sausage mixture.
Garnish and enjoy: Sprinkle with chopped fresh basil or parsley, additional Parmesan cheese if desired, and serve immediately.