In a large pot of boiling salted water cook rigatoni or fusilli pasta with one tablespoon of oil until al dente. Drain.
Meanwhile, in a large saucepan melt butter or margarine. Stir in flour and milk and whisk until mixture boils and thickens. Add grated Parmesan cheese, salt, garlic salt, nutmeg, thyme and grated Cheddar cheese and stir until blended.
Add cooked broccoli and drained pasta to cheese sauce. Mix well. Pour into a greased 9x13 inch baking dish. Sprinkle with grated Swiss cheese.
Bake uncovered at 350 degrees C(175 degrees C) for 20 minutes. Let stand 10 minutes before serving.