Cook fettuccine according to the package directions; drain. Meanwhile, bring a pot of salted water to a boil and cook broccoli stalk (cut into florets, stalk peeled and sliced), 3 minutes; drain. Heat skim milk and butter in a large saucepan over low heat. Slowly whisk in flour. Simmer until slightly thickened, whisking constantly, 1 to 2 minutes. Remove from heat and stir in Parmesan and kosher salt. Add the pasta and broccoli and stir over low heat until heated through. Top each serving with Parmesan shavings.