Cook the Pasta
Bring a large pot of salted water to a boil and cook the penne pasta for 2 minutes less than the recommended time. This is crucial for preventing mushiness. Drain the pasta and set it aside.

Season and Cook the Chicken
In a medium bowl, toss the cubed chicken breast with 1 1/2 teaspoons of Cajun seasoning until fully coated. In a large, deep skillet (or Dutch oven) over medium-high heat, melt 1 tablespoon of butter. Add the seasoned chicken and cook for 7–8 minutes, stirring occasionally, until fully cooked through and golden brown. Remove the chicken from the skillet and set it aside.

Sauté the Aromatics
To the same skillet, add the remaining 2 tablespoons of butter and the olive oil. Once melted, add the sliced red bell pepper, green bell pepper, red onion, minced garlic, and 1 teaspoon of Cajun seasoning. Cook for 3–4 minutes, stirring often, until the vegetables are slightly softened. Remove the vegetables and set them aside with the chicken.

Build the Roux and Sauce Base
Add the remaining 2 tablespoons of butter to the empty skillet. Once melted, add the all-purpose flour and stir well. Continue cooking for 3–4 minutes, stirring frequently, to remove the raw flour taste. Whisk in the chicken stock, milk, coarsely chopped roasted garlic, salt, and black pepper. Stir vigorously until the mixture is smooth and lump-free. Bring to a simmer, reduce heat to low, and cook for 8–10 minutes, stirring often, until the sauce thickens.

Finish and Serve
Stir the grated Parmesan cheese and heavy cream into the sauce until velvety smooth. Add the cooked chicken, sautéed vegetables, and the par-cooked pasta back into the skillet. Stir until all ingredients are well combined and coated. Cook for 2–3 minutes, or until piping hot. Garnish generously with chopped green onions before serving.