Sear the sausage. Heat a large, heavy-bottomed skillet over high heat. Add the olive oil and swirl to coat the bottom of the skillet. Once your pan is hot, add the sausage to the skillet in a single layer. Allow the sausage to sear for 1-2 minutes before flipping to sear on the other side (see notes). Remove sausage from the skillet and set aside.
Cook the chicken. Return skillet to medium-high heat. Add one more tablespoon of olive oil to the skillet, swirl to coat, and add the chicken in a single layer. Sprinkle with salt, pepper, and 1 tablespoon of Cajun seasoning. Allow the chicken to cook, undisturbed, for 2 minutes before stirring. Continue to sauté the chicken for 3-4 minutes, stirring often, until cooked through. Transfer to a clean plate and set aside.
Cook the onions. Return your skillet to medium heat. Add additional olive oil, if needed, and add the finely minced onion to your skillet. Cook the onion, low and slow, stirring occasionally, for 4-5 minutes, or until soft and translucent. Add the minced garlic and sprinkle with the remaining tablespoon Cajun seasoning, dried rosemary, and a pinch of salt. Mix well to combine and cook, stirring continuously, for 1 minute.
Add the broth and beans. Add the chicken broth and drained kidney beans to the onions. Bring to a simmer then add the sausage and chicken back to the skillet. Mix well to combine and continue to cook for 1-2 minutes or until heated through. Season with salt and pepper, to taste, and serve with cooked white or brown rice, if desired.