For muffins: Make muffins according to package directions and stir cheddar and chives into batter. Fill greased muffin tins and bake for time stated on package. If using a larger package of cornbread (12 to 16 oz.), double the cheddar and chives.
For jambalaya: In a medium saucepan, bring chicken broth, garlic, and 2 tsp. Cajun seasoning to a boil. Stir in rice. Lower heat to a simmer, cover, and cook for 15 to 20 min., or until broth is absorbed and rice is tender. Turn off heat and let stand, covered, for 5 min. Remove lid and fluff rice with a fork to let steam escape while you prepare sausage. Toss sausage slices with 1 Tbsp. Cajun seasoning. Heat 1 Tbsp. oil in a 12-inch cast iron skillet (or other heavy-bottomed pan) over medium-high heat. Add sausage and cook 5 min. per side, or until pieces start to blacken. Transfer blackened sausage to a plate. Add celery, bell pepper, and onion to the hot skillet. Season with salt & pepper and cook for 3 to 4 min. Transfer veggies to plate with sausage. Add butter and remaining 2 Tbsp. vegetable oil to skillet and heat until butter is melted. Press cooked rice evenly into the pan and let cook undisturbed for 5 to 7 min. Use a spatula to gently lift up rice to check for desired crispness (the rice should be a light brown). Flip rice (a section at a time) to crisp the other side. Cook another 5 to 7 min. The rice will turn darker brown and may blacken in some spots. Stir in blackened sausage, veggies, and tomato. Again, press rice evenly into the pan and cook for another 6 to 7 min. Garnish with parsley and your favorite hot sauce to taste. Serve with cornbread muffins.