Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Sprinkle both sides of chicken breast with 1/2 teaspoon Cajun seasoning, or to taste.
Grill chicken breast and pork sausage on the preheated grill until browned and no longer pink inside, about 5 minutes per side. Transfer to a plate and let rest for 5 minutes. Cut chicken and sausage into bite-size pieces.
Bring a large pot of lightly salted water to a boil. Cook the farfalle pasta at a boil, stirring occasionally, until cooked through yet firm to the bite, about 12 minutes; drain.
Melt butter in a large skillet over medium heat. Cook and stir green bell pepper, red bell pepper, onion, and garlic in hot butter until slightly softened, 2 to 3 minutes. Stir chicken and sausage pieces into vegetables, reduce heat to medium-low, and pour 1 cup half-and-half into skillet. Stir to combine.
Mix cornstarch into remaining 1/2 cup half-and-half in a small bowl until smooth; pour into skillet and stir until sauce simmers and thickens, about 5 minutes. Toss cooked farfalle pasta into mixture until coated; season with additional Cajun seasoning and dried basil.