Season the chicken breasts with salt and pepper. Place the flour in a shallow bowl and dredge each breast, coating evenly and shaking off the excess. Set aside.

In a large frying pan over medium-high heat, melt 1 tablespoon of the butter with the oil until very hot. Add the chicken breasts and cook, uncovered, until the undersides are golden brown, 6-8 minutes. Turn the chicken breasts over and continue cooking until they feel firm when pressed in the centers and juices run clear, about 6 - 8 minutes longer. Depending on the size, you may need even 10 - 15 minutes. Don't let them burn.

Reduce the heat to very low. Sprinkle the breasts evenly with the chopped sage. Top each breast with a piece of prosciutto, then divide the cheese slices evenly among the breasts. Cover the pan tightly and cook until the cheese is melted, about 1 1/2 - 2 minutes. Transfer to a serving platter and tent with aluminum foil, being careful not to allow the foil to touch the cheese. It will stick.

Raise the heat to high. When the pan is sizzling, add the wine and deglaze the pan, stirring with a wooden to scrape up any browned bits stuck to the pan bottom. Boil until reduced to 1/4 cup, about 3 minutes. Remove from the heat and whisk in the remaining 1 tablespoon butter.

Spoon an equal amount of the sauce over each breast, then garnish with a sage leaf, if desired. Serve at once.