Mornay is simply a traditional Béchamel sauce with the addition of shredded or grated cheese.
2 tablespoons butter
2 tablespoons all-purpose flour
1 1/2 cups hot milk
1/2 cup (2 ounces) shredded Gruyere or Swiss cheese
1/2 cup (2 ounces) freshly grated Parmesan cheese
Dash ground nutmeg
Salt and freshly ground pepper to taste
Dash of cayenne pepper
Melt butter in a heavy saucepan over low heat. Add flour and cook slowly for about 2 minutes, stirring constantly. Remove from heat. The mixture should get foamy or frothy but not brown.
Add the hot milk and whisk vigorously until smooth. Add the seasonings and return to the heat and boil for about 1 minute over medium high heat. Remove from heat, add cheeses and stir until incorporated completely. Add cayenne.
Makes about 2-1/4 cup.