When pounding the chicken with the mallet, use smooth and firm but even strokes in a down and away motion to avoid tearing the meat.
In a saucepan, bring the milk and garlic to a gentle simmer over medium-low heat. Strain the hot milk into a medium bowl. In the same saucepan, melt the butter over medium-high heat. Add the flour; whisk until blended. Cook for a minute or two, whisking constantly. Whisk in the hot milk; season with salt, white pepper, and nutmeg. Add the cheeses and stir until melted, 1 to 2 minutes. Cover the sauce and keep warm over low heat.
Using a sharp knife and starting from the longer, wider side of each chicken breast, cut horizontally about three-quarters of the way through. Open each piece like a book to make 4 large cutlets. Using a meat mallet, pound the cutlets between sheets of plastic wrap to flatten each piece into an 1/8- to 1/4-inch-thick cutlet. In a shallow dish, season the flour with salt and pepper. In another shallow dish, season the eggs and beat until blended. In a third shallow dish, mix the breadcrumbs, cheese, herbs, and lemon zest.
In a large skillet, heat about 1/8 inch of olive oil over medium-high. Place a wire rack inside a rimmed baking sheet.
Coat the cutlets in the flour, then the eggs, and then the breadcrumbs, pressing so the crumbs adhere. Add 2 cutlets to the oil. Fry until deep golden, 5 to 6 minutes per side. Transfer to the wire rack. Repeat with more oil and the remaining cutlets.
Divide the cutlets among plates. Top with the cheese sauce. Top each cutlet with 2 gently furled slices of prosciutto. Serve with the salad, if desired.
To quickly make chicken cutlets, cut the breasts horizontally almost in half and open each like a book before you grab a mallet.