Take your slices of meat and, placing them between two sheets of waxed paper, give them a good thumping with the back of a heavy skillet—or with a meat pounder, if you have one. This will thin them out even more and break down some of the fiber in the meat, rendering it more tender.
Meanwhile, heat the butter (or butter and oil, or even just oil if you'd rather) in a skillet over medium-high heat. When the foam subsides, add the slices, which you will have very light floured just beforehand. Make sure they are not crowded in the pan or they will not brown properly. (If your skillet is not big enough to hold all the slices at one go, you can proceed in batches.) Sear them for just 30 seconds or so on each side, seasoning well with salt and pepper. They should lightly brown around the edges. Remove the slices to a heated platter and keep warm. (A toaster oven set to 'warm' is perfect for this.)
Add the marsala to the pan, scraping up any browned bits from the bottom of the skillet. Let it reduce until it forms a syrupy sauce. Then, turning off the heat, add the slices back to the pan and turn them around to coat well.
Arrange the slices on a warmed platter, pour over any remaining sauce in the skillet, and serve immediately.