Cook pasta according to package directions until al dente, reserving 1 cup pasta water before draining.
While pasta cooks, melt butter in a large skillet over medium heat and sauté garlic until fragrant, about 1 minute.
Add heavy cream, chicken broth, sun-dried tomatoes, Italian seasoning, and red pepper flakes to the skillet and bring to a simmer.
Stir in Parmesan cheese until melted and smooth, then add the shredded rotisserie chicken and cook until heated through, about 3-4 minutes.
Add drained pasta to the sauce and toss to combine, adding reserved pasta water as needed to reach desired consistency.
Season with salt and pepper to taste, garnish with fresh basil, and serve immediately.