01 - 
                Season chicken pieces with salt, freshly ground pepper, and Cajun seasoning to taste. Allow to sit for several minutes to absorb the flavors.
              
              
              
                02 - 
                Cook penne pasta in a large pot of salted boiling water until al dente, according to package instructions. Drain and set aside. Separately, steam or blanch broccoli florets until tender yet vibrant green; set aside.
              
              
              
                03 - 
                In a large skillet or pot, heat butter and olive oil over medium-high heat. Add the seasoned chicken in a single layer and sauté for approximately 5 minutes per side, or until fully cooked and golden. Remove chicken and reserve.
              
              
              
                04 - 
                Reduce heat to medium. Add minced garlic to the skillet and cook for 30 seconds to 1 minute until fragrant. Pour in heavy cream, then gradually stir in milk while mixing constantly to avoid curdling. Bring the mixture to a gentle simmer.
              
              
              
                05 - 
                Once hot, gradually incorporate the grated cheese, stirring until the cheese is fully melted and the sauce is smooth and cohesive.
              
              
              
                06 - 
                Add the cooked pasta, sautéed chicken, and prepared broccoli to the sauce. Stir thoroughly to coat all ingredients evenly in the sauce. Taste and adjust seasoning with additional Cajun seasoning, salt, or pepper as needed. Warm through for 1–2 minutes.
              
              
              
                07 - 
                Plate the dish while hot. Optionally garnish with extra cheese, freshly ground black pepper, or chopped parsley as desired.