Heat milk in large pan over medium heat til you see bubbles forming on top. Meanwhile, melt butter in another pan and stir in flour to make a roux.
Add warm milk, whisking constantly and continue cooking til mixture thickens, about 5 minutes. Add cheese, whisking constantly to mix. Season with cayenne and salt and pepper to taste. Strain through a sieve to remove any lumps before serving.
Makes 3 cups.