Prepare chicken by slicing it thin and pounding it out with a meat tenderizer. Season both sides of the chicken with salt and pepper.
Top each chicken cutlet with 1 sage leaf and then a slice of prosciutto. Smack the prosciutto on, to make it stick. When I say smack it on, I'm being literal. Place the prosciutto over the sage and smack it. This will adhere it to the chicken.
In a large frying pan, heat 2 tablespoon of extra virgin olive oil over medium-high heat. Dredge the chicken in flour. Place the chicken, prosciutto side down for 30 seconds, and then flip to the chicken side. You want the prosciutto to become crispy but not overcook.
Pan fry the opposite side for 3-4 minutes until the chicken becomes golden brown. Transfer the chicken to a cooling rack.
Add 1 tablespoon of olive oil to the same pan you cooked the chicken and lower the heat to medium. Take sage leaves and stir them in the olive oil for fifteen seconds. Then add in the lemon juice and white wine. Bring to a simmer and use a wooden spoon to break up all the brown bits on the pan.
Once the sauce is simmering, return the chicken to the sauce and simmer until the chicken reaches 160°F. Then remove the chicken from the sauce.
Turn off the heat and add the chopped cold butter to the sauce. Keep stirring until the butter complete mixes emulsifies with the sauce. Return the chicken to the sauce or pour the sauce over your chicken and serve!
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Notes
Dredge in flour immediately before frying. If you dredge even 10 minutes in advance, the chicken will start to soak up the flour and be more likely to stick to the pan.
When searing the prosciutto side, you're trying to get the slightest crust on the prosciutto. You're not cooking it. So just 30 seconds on that side is plenty.
It is very easy for the white wine sauce to separate and become oily. It should be an opaque yellowish color. If you start seeing the oil separate, add 2 tablespoon of water. Stir it and it should come together and look yellowish and creamy again.
The prosciutto and chicken naturally hold together, but you can use a toothpick to thread through the prosciutto and chicken to help it stick if you are worried about it.