Place the flour on a large plate. Place each scaloppine in the flour and pat gently to remove the excess. Place on a separate plate. Repeat until all the meat is coated.
Heat olive oil and butter in a large skillet over medium heat. Place a few scaloppine in the pan and cook for 2 to 3 minutes on the first side, then 1 to 2 minutes on the second side. Sprinkle lightly with some sea salt. Remove to a large plate. Repeat with remaining pieces.
To the same pan, add onion and cook for 5 minutes, stirring occasionally. Add mushrooms and cook for 5 more minutes, stirring occasionally. Add Marsala, Madeira and dry Sherry scraping pan to incorporate all the drippings. Let simmer until the liquid has reduced by half, about 3 minutes.
Reduce heat to low, add cream and cooked scaloppine. Stir to warm the meat. Serve immediately.
HELPING HANDS: Kids can help flour the scaloppine.