Prepare the linguine according to the package directions in a 3-quart saucepan. Add the broccoli during the last 4 minutes of the cooking time. Drain the linguine and broccoli well in a colander.
Heat the butter in a 10-inch skillet over medium-high heat. Add the chicken and cook until it's well browned, stirring often.
Stir the soup, milk, cheese, black pepper and linguine mixture into the skillet. Heat, stirring occasionally, until the mixture is hot and bubbling. Serve with additional Parmesan cheese.
Grilled Chicken & Broccoli Alfredo: Substitute grilled chicken breasts for the skinless, boneless chicken.
Shrimp & Broccoli Alfredo: Substitute 1 pound fresh extra large shrimp, shelled and deveined for the chicken. Cook as directed in Step 2 until the shrimp are cooked through.
Spanish-Inspired Tip: Reduce the chicken to 1/2 pound and omit the Parmesan cheese. Prepare as directed above. Stir 1/2 pound peeled cooked shrimp, 1/4 pound chorizo or ham, diced and 1 teaspoon paprika into the skillet in Step 3.
Indian-Inspired Tip: Omit the Parmesan cheese. Substitute 1 cup uncooked basmati rice for the linguine. Prepare as directed above. Stir 1 teaspoon curry powder and 1/2 teaspoon ground cumin into the skillet in Step 3. Sprinkle with toasted slivered almonds, if desired.
Asian-Inspired Tip: Omit the Parmesan cheese. Substitute 1 package (6 ounces) rice noodles for the linguine. Prepare as directed above. Stir 1 tablespoon soy sauce, 2 cloves garlic, minced and 2 teaspoons minced fresh ginger root in to the skillet with the chicken in Step 2.