Lightly pound the cutlets between 2 sheets of wax paper with a mallet or rolling pin until thin but not torn. Sprinkle with sage and salt. Top with prosciutto and cheese slices. Roll up cutlets from short sides and secure with toothpicks. Refrigerate, covered, for 1 hour or overnight.
COOK THE CHICKEN:
Heat a large nonstick skillet over medium-high heat. Swirl in the oil and butter, then add the chicken rolls. Cook until lightly browned, about 2 minutes on each side. Transfer the rolls to a plate. Add the onion to the same skillet and cook, stirring occasionally, until golden 7 to 10 minutes. Add the Marsala and the browned chicken rolls to the skillet; bring to a boil. Reduce the heat and simmer, covered, until just cooked though, about 8 minutes.