Cook the linguine according to package instructions until al dente; drain and keep warm.
Pat the chicken strips dry and season lightly with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Heat 1 tablespoon oil in a large skillet or cast-iron pan over medium heat.
Add the chicken strips and cook, turning occasionally, until seared and cooked through, about 5–7 minutes.
Sprinkle 2 teaspoons Cajun or Adobo seasoning, 1/2 teaspoon dried basil, 1/4 teaspoon garlic powder, and optional 1/4 teaspoon smoked paprika over the chicken; stir to coat and cook 30–60 seconds to bloom the spices.
Reduce heat to low and pour in 1/2 cup heavy whipping cream, then stir in 1/4 cup shredded Parmesan; simmer 2–3 minutes until the sauce is warmed and slightly thickened.
Add the cooked linguine (and drained sun-dried tomatoes if using) to the skillet and toss gently to coat the pasta evenly with the sauce and chicken.
Serve immediately, topping with additional Parmesan and chopped green onions if desired.
Tip: Put pasta in a bowl and toss with the sauce before plating to ensure even coating and avoid sauce pooling on the plate.