The flour must cook before adding the cream. Once I add the flour, I cook it with the butter for roughly 5-10 minutes, depending on how much I'm making. Smell it before adding the cream. It shouldn't smell like raw flour. If it does, keep cooking it. Then add the cream, the cheese, etc.

Sounds like your problem is not letting the flour cook long enough in the butter before adding the milk - that's what usually produces a floury taste in bechamel based sauces.

I think what you are referring to would be called sauce mornay. You begin by making a bechamel which begins with a roux. Heat your butter in a sauce pan. Using a wooden or silicone spoon mix together slowly until you get a light brown color. Meanwhile on a separate burner heat up milk to just below the simmering point. It should scalded but not boiling (a little skin will like start to form on the top).Stir that into the roux and blend thoroughly. Add your grated cheese. Grab a whisk and stir until smooth. A little grated nutmeg can't hurt.