In a medium sized frying pan, heat the olive oil over medium heat until almost smoking.
Season the flour with salt and pepper and place in a shallow dish (such as a rimmed soup bowl). Put each veal piece in the flour one at a time and turn over to completely cover with flour. Add to the pan and sautée, turning once, until golden brown on both sides, about 2 minutes per side. Remove the veal to a side plate.
Add the mushrooms to the pan and sautée until they are lightly browned and the juices have evaporated. Add the Marsala, bring to a boil, and reduce by one third. Add the cold butter and replace the veal in the pan. Bring just to a boil, reduce the heat, and simmer for 5 to 6 minutes. Stir in the thyme and check the sauce for seasoning.
Drizzle the mushroom sauce over the veal and serve.