In a large, heavy bottom pot or skillet, cook the bacon until crisp. Using a slotted spoon, transfer bacon to a paper towel-lined plate.
If there aren't 2 tablespoons of drippings remaining in the skillet, add more bacon fat or vegetable oil to make up the difference. Add sausage to the skillet, and cook over medium heat, until browned. Using a slotted spoon, transfer to the plate with bacon.
In a small bowl, mix together with a fork Cajun seasoning, old bay, and dried thyme until evenly combined.
Add potatoes, onion, and red and green pepper to the pot. Sprinkle seasoning mixture over vegetables to evenly coat. Cook over medium heat, tossing them every 3-4 minutes, until the veggies become nicely golden browned. Add garlic and continue to cook, stirring and flipping the mixture, for about 1 minute. Return bacon and sausage to the skillet and toss to combine.
Return bacon and sausage to the skillet. Pour in the chicken broth over vegetables and dot the top with butter. Cook over medium, covered, stirring occasionally, until potatoes are tender, about 6-9 minutes.
Remove lid, continue to cook uncovered if any chicken broth remains. Taste and adjust seasoning (I use about 1/2 teaspoon salt per our taste). Transfer to a serving dish, garnish with parsley and, or fresh thyme and serve.