Can be prepared in 45 minutes or less.
In a large heavy skillet cook garlic and herbs in butter and oil over moderate heat, stirring, until garlic is softened but not browned. Remove skillet from heat. Add brandy and ignite, being careful as flames shoot up. Shake skillet gently until flames die out. Return skillet to moderate heat and stir in cream.
Add cheeses, 1 at a time, stirring until each cheese melts before adding the next. Cook sauce at a bare simmer until thickened slightly, about 8 minutes. Keep sauce warm.
In a kettle of boiling salted water cook pasta until al dente and reserve about 1/2 cup cooking water. Drain pasta well and in a bowl toss pasta with sauce and enough reserved cooking water to reach desired consistency.