Whisk together flour and 1/4 cup milk. Add flour mixture to remaining milk, whisking until smooth.
Bring milk mixture to a boil in a large skillet over medium heat; reduce heat to medium-low, and simmer, whisking constantly, 3 to 5 minutes or until smooth. Stir in cheese and next 4 ingredients until smooth. Stir in pasta, and cook 1 minute or until thoroughly heated. Serve immediately.