Heat 1 tbsp oil and 1 tbsp butter in a large skillet over medium-high heat. Place 2 pieces of dressed, floured chicken – sage/prosciutto side down – in the skillet. Cook 3-4 minutes on one side, until prosciutto is crispy and darkened and the chicken has been seared brown, then flip. Cook on the other side 3-4 minutes, or until chicken is cooked through.
Remove cooked chicken to the paper-towel lined plate and set aside.
Add another 1 tbsp oil and 1 tbsp butter to the skillet, then repeat the cooking process with the remaining two chicken breasts.
Once the second batch of chicken is removed from the skillet, turn off the stove. Drain the butter and oil from the skillet, then return the skillet to the stovetop.
Pour the marsala wine into the pan, THEN turn the stovetop heat on high. Deglaze the skillet with the marsala wine, scraping up any browned bits. Let simmer 1-2 minutes, or until wine is reduced by half.
Add the chicken broth to the skillet and let simmer on high heat for 3 minutes, until the mixture has reduced by half.
Reduce the heat to medium and stir in the remaining 1 ½ tbsp butter to the skillet until completely melted. Let marsala sauce simmer 1-2 more minutes, until slightly thickened. Transfer sauce to a small pitcher or bowl for serving with the Chicken Saltimbocca.
Transfer the chicken breasts to a platter and serve immediately; marsala sauce can be served on the side or drizzled on top. Great sides for Chicken Saltimbocca are polenta or pasta.