Add a little nutmeg to taste.
Cook until onion is tender, being careful not to scorch the milk.
Drain, reserving the milk and discarding the onion.
In the saucepan, melt butter over medium heat.
Whisk in flour and cook for 1-2 minutes to form a roux, without browning.
Gradually whisk in milk, continuing to whisk until the mixture is smooth and begins to thicken.
Season with salt, pepper, and a pinch of nutmeg, if desired.
Cook the Chicken Cutlets: ---
In a large oven-safe skillet, heat vegetable oil to 375°F
Add the breaded chicken cutlets and cook until golden brown on both sides, about 3-4 minutes per side.
Transfer the skillet, with a slice of Provalone cheese on each cutlet, to the preheated oven and bake until the cheese melts, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).