Bring that quart of cold water to a rolling boil in your large pot. Add the sea salt, stir, and once it returns to boil, add penne. Cook it for about 2 minutes less than package directions so it ends up just shy of al dente. Drain and set aside, but reserve a splash of pasta water just in case.
Toss the chicken pieces with 2 tsp Cajun seasoning. In your skillet, heat the avocado oil over medium-high heat. Add chicken and sear until cooked through and slightly golden (about 5–7 minutes). Remove from the skillet and set aside.
In the same skillet, add red bell pepper, jalapeño, onion, and garlic (use a little extra oil if needed). Sauté until vegetables are softened and fragrant (about 3–4 minutes). Then remove them and set aside with the chicken.
Lower heat to medium, then melt butter in the skillet. Whisk in the flour and stir constantly for about a minute until the mixture is bubbly and golden. Gradually whisk in half-and-half, continuing to stir until smooth. Let it thicken over 3–5 minutes.
Once the sauce begins to thicken, stir in Parmesan cheese, Cajun seasoning (½ tsp), salt, and black pepper until melted and smooth. Add mozzarella and lime juice. Then fold in cooked pasta, chicken, and veggies. Toss gently until well coated and heated through.
Transfer to serving plates or into a bowl. Sprinkle chopped cilantro on top if using. Serve immediately while piping hot and creamy.