Place the thin veal slices on wax paper. Sprinkle the cheese over the meat and cover with wax paper. Press the cheese well into the meat.
Remove top wax paper and place a slice of prosciutto on top of the cheese. Brush on brandy and roll up carefully, securing with string.
Place the butter and oil in a large skillet. When sizzling, brown the veal rolls on all sides.
Remove the meat and to the juices in skillet add the garlic, thyme, salt, pepper, tomato paste, beef broth, and Marsala wine. Stir to combine the ingredients and bring to a boil. Return the veal rolls to the pan. Reduce heat, cover skillet, and simmer for about 15 minutes, or until tender. Transfer the veal to a hot platter and remove the strings. Cover loosely with foil.
In another pan, melt 2 tablespoons of butter until hot but not smoking, and sauté the mushrooms. Set aside.
Add the lemon juice to the pan used to sauté the veal, and adjust seasoning. Mix the cornstarch with a little water and add gradually to the sauce, stirring constantly and adding just enough of the cornstarch mixture to thicken the sauce slightly.
Pour the sauce around the Saltimbocca, and garnish with the mushroom caps. Sprinkle parsley over the finished dish.