Bring a large pot of salted water to a boil. Cook pasta according to package directions, adding peas during the last 2 minutes of cooking time. Reserve ½ cup pasta water, then drain.
Meanwhile, melt butter in a large skillet over medium heat. Add garlic and cook, stirring, until fragrant, 1 to 2 minutes. Add flour and cook, stirring, 1 minute. Slowly whisk in milk, stirring constantly. Cook, stirring occasionally, until thickened, 3 to 4 minutes. Season with salt and pepper.
Stir in pasta and peas, chicken, Parmesan, and basil. Stir in reserved pasta water, 1 tablespoon at a time, as needed to make a sauce. Garnish with basil. Serve immediately.