In 1 quart saucepan, melt the butter and sauté the onion in the butter for about 2 minutes or until tender. Stir in the flour and a dash of white pepper.
Add the milk, then cook and stir over medium-heat until thick and bubbly. Continue cooking and stirring for 1 minute more.
Reduce the heat to low. Stir in the cheese just until melted. Remove from heat at once. Stir in the wine.
If the mixture is thick, stir in 1 to 2 more tablespoons of milk.
Notes
If you don't wish to use wine in the recipe, substitute 1 teaspoon lemon juice.