Prepare the sauce by heating the butter in a medium saucepan until it foams. Add the flour and stir well until the flour takes on a blond color. Add the milk and half and half, stir well to blend. Reduce heat and simmer the sauce until it starts to thicken. Add the shredded cheese and stir to melt. Season with a pinch of nutmeg and salt and pepper to taste. Turn heat down to warm, cover pot.
Stir the milk and cream into the flour and butter roux.
While sauce cooks, lightly toast Texas Toast.
Brine the turkey breast overnight in 1 cup kosher salt and ½ cup white sugar dissolved in 1 gallon of water.
Slice the breast into 5 cutlets, pound flat with meat mallet
Pound the turkey cutlets flat with a meat mallet.
Dredge the turkey cutlets in seasoned flour, rest on wire rack for 5 to 10 minutes while you heat a quarter inch of vegetable oil in an iron skillet over medium-high heat. Fry the cutlets for 3 to 4 minutes per side or until just cooked through. Fry in batches so as not to crowd the skillet. Place finished cutlets on a warm platter and cover with foil.
Dredge the turkey cutlets in seasoned flour and fry till crisp and just cooked through.
While the oil is still hot, flash fry the slices of country ham to lightly crisp, 30 seconds to a minute per side. Drain them on a paper towel.
Thinly sliced country ham replaces bacon in this version.
To assemble the sandwich, plate a slice of toast. Top the bread with a turkey cutlet, then a slice of country ham. Spoon Mornay over the sandwich. Top with a slice of tomato and a runny fried egg. Tip: If your sauce has over thickened while you worked on the rest of the sandwich, simply stir in some additional milk or half and half to thin it back down.