Preheat oven to 350°F.
Arrange the slices of prosciutto on a large baking sheet lined with parchment paper without overlapping them. Bake 10-15 minutes until crispy and deep reddish brown in color; let cool. Switch on broiler.
Butterfly each chicken breast by cutting into them on the fuller side with a very sharp knife. Split them open but do not cut all the way through horizontally, so you can open the breast like a book. Place a plastic food storage bag over top of the breast (it’s thicker than plastic wrap. Don’t place the breast in the bag unless you will be freezing the breast). Pound the breast with smooth, even strokes until chicken is 1/8- to 1/4-inch thick. Season with salt and pepper on both sides, repeat.
Stem chard or spinach by pulling the leaves down and away from stalk. Pile greens together and cut across in 2-inch strips to coarsely chop.
Zest 2 teaspoons of lemon zest and halve the lemon.
Heat a large, nonstick 12- to 14-inch skillet over medium-high heat with EVOO, 2 turns of the pan. Add chicken breasts, 2 at a time and brown about 3 minutes on each side, remove to baking sheet and cover with foil, repeat.
Reduce heat a bit and add more EVOO, 2 turns of the pan. Add garlic and swirl 1 minute, add greens in stages to wilt. Season with salt and pepper and sprinkle with lemon zest. Once wilted, douse pan with juice from half a lemon. Remove pan from heat.
Using tongs, shake off all excess liquid from the greens and arrange them on top of the chicken leaving a small rim around the greens so you can see the chicken. Layer or shingle 2 thin slices of cheese over the greens and broil to melt, brown and bubble the cheese.
Place spinach-and-cheese-topped chicken on dinner plates and top with 3 pieces of crispy prosciutto each.