Place a large, tall-sided skillet with 1 to 2 inches of water over high heat and bring up to a boil to cook the asparagus.
Working with one chicken breast at a time, line the breast with the tip closest to you. Place your hand flat on top of it and, with a very sharp knife, cut into the center of the thickest part of the breast. Carefully and slowly, work your way down to the tip end, cutting into the chicken. The goal is to butterfly the breasts, cutting them just shy of completely in half. Open up the chicken breast as if it were a book and pound it out slightly under a piece of plastic wrap with a heavy skillet. Repeat with the remaining chicken.
In a small bowl, combine the thyme, lemon zest and parsley. Lay each butterflied chicken breast out on a flat work surface so each breast is open. Sprinkle the insides of each chicken breast with the thyme and lemon zest mixture. Add a slice of proscuitto cotto to each piece and top with a slice of fontina cheese.
Fold each piece over to enclose the ham and cheese in the chicken breasts. Season with salt and freshly ground black pepper.
Preheat a large skillet over medium-high heat with 3 turns of the pan of EVOO, about 3 tablespoons. Add the seasoned, stuffed chicken breasts to the hot skillet and brown for 5 minutes.
Gently flip the chicken over and continue to brown for another 5 minutes. Add a 1/2 cup of dry white wine to the skillet and cook until the wine has reduced by half.
Once you have the chicken working in the skillet, add a generous amount of salt to the skillet with the boiling water. Simmer the spears for 3-5 minutes until just tender. Drain the asparagus and squeeze the lemon juice over the top.
To serve, plate asparagus, top with the chicken breasts and spoon sauce over the top. Yum-O!