Melt butter in skillet and saute the onions until tender but not brown.
Remove from pan and set aside.
In the same pan, melt 6 tablespoons of butter, and stir in the flour, making a smooth thick roux.
Add scalded milk and salt and stir until thick and smooth.
Add onions and set aside.
Butter each slice of bread on one side.
On the unbuttered side, place a slice of cheese and a slice of ham.
Cover with another slice of bread with the butter on the outside.
Grill in heavy skillet, pressing together as you would a grilled cheese sandwich.
Cut each sandwich into 4 squares and place in an oven-proof dish or on a cookie sheet.
Top each with a tablespoon of the sauce, then sprinkle generously with grated cheese.
Glaze under broiler until browned.