Ground veal should be from the shank, neck, or shoulder, because these cuts are moist and sweetly flavored. Veal is lovely grilled and lends itself to gentle seasonings—and even when formed into burgers, retains its elegance.
Heat the olive oil in a skillet over medium-high heat. Add the mushrooms and cook, stirring for about 1 minute, or until they begin to soften. Add the garlic, salt, and pepper and cook for 2 to 3 minutes, or until the mushrooms soften. Set aside to cool.
Combine the veal, parsley, cooled mushroom mixture, salt, and pepper in a large bowl. Using your hands, mix well. Form into 6 patties. Refrigerate until ready to grill.
Prepare a charcoal or gas grill. Lightly spray the grill rack with vegetable oil cooking spray. The coals should be modestly hot.
Grill the burgers for about 8 minutes. Turn and grill for about 6 minutes longer for medium-well burgers.