Melt the butter in a heavy bottomed sauce pan on medium heat.
Stir in the flour and cook stirring constantly until the paste cooks and bubbles a bit, about 2 minutes, but don't let it brown.
Slowly add the heated milk, continually stirring as the sauce thickens.
Bring to a boil.
Add the cheese, salt & pepper and the cayenne pepper, lower the heat and cook stirring constantly for 2-3 minutes.
Remove from heat.
To cool this for later use, cover it with wax paper, or pour a film of milk over the top to prevent skin from forming on top.
Chef's notes: Makes about 2 ¼ Cups. White cheese such as Pepper Jack, Mozzarella, Swiss, or parmesan can be used. To prevent skin from forming when cooling, cover with wax paper or pour a film of milk over the top.