Bring a large pot of salted water to a boil. Cook linguine according to package directions until al dente. Reserve 1/4 cup of pasta water and drain the rest.
While pasta cooks, season the cubed chicken with 1/2 tablespoon of the Cajun seasoning.
In a large skillet over medium-high heat, melt 1 tablespoon of butter. Add the chicken and cook until browned and cooked through (about 6-8 minutes). Remove chicken from the skillet and set aside.
Reduce skillet heat to medium. Add the remaining 1 tablespoon of butter and the minced garlic. Sauté for 1 minute until fragrant.
Pour in the heavy cream and the remaining 1 tablespoon of Cajun seasoning. Bring to a gentle simmer.
Add the cubed Velveeta cheese to the skillet. Stir constantly until the cheese is completely melted and the sauce is smooth.
Incorporate the cooked chicken and the cooked linguine into the sauce. Toss to coat thoroughly. If the sauce is too thick, add the reserved pasta water 1 tablespoon at a time until desired consistency is reached.
Season with black pepper and garnish with chopped parsley before serving.