Chop rotisserie chicken into bite-sized cubes.

Heat oven to 350°F. Cook and drain spaghetti as directed on package, adding peas during last 3 minutes of cooking.

Meanwhile, in large Dutch oven or saucepan, melt butter over low heat. Stir in flour, salt, and pepper. Cook, stirring constantly, until mixture is smooth and bubbly (you might have to increase heat to medium-low).

Stir in broth and whole milk. Heat to boiling, stirring constantly. Boil and stir until slightly thickened (about a minute or two). Stir in spaghetti, peas, and chicken.

Sprinkle with cheese. Bake uncovered for about 30 minutes.