Melt butter and add enough flour to make a reasonably thick roux (enough to absorb all of the butter). Add milk and 6 tablespoons Parmesan. Add egg to thicken sauce, but do not allow to boil.
Remove from heat. Fold in whipped cream. Add salt and pepper to taste.
For each Hot Brown, place 2 slices of toast on a metal (or flameproof) dish. Cover the toast with mushrooms and thinly sliced tomatoes, then cover with a liberal amount of turkey. Pour a generous amount of sauce over the turkey and toast. Sprinkle with additional Parmesan. Place entire dish under a broiler until the sauce is speckled brown and bubbly. Remove from broiler, cross 2 pieces of bacon on top and serve immediately.