Special equipment: Four 12-inch skewers
Prepare a grill for medium-high heat.
Process the mushroom stems and half the parsley in a food processor until nearly pureed, about 20 seconds; transfer to a medium bowl. Add the sausage, breadcrumbs, grated Parmesan, garlic, oil, 1/2 teaspoon salt and a few grinds of pepper to the bowl, and mix until combined.
Stuff each mushroom cap with 1 to 2 teaspoons of the filling, depending on the cap's size. Give a gentle push to make sure the filling adheres to the cup of the mushroom and mounds a bit over the top. Thread a skewer through the centers of 8 of the stuffed caps; the caps should be touching and relatively snug on the skewer. Repeat with the remaining skewers and mushrooms.
Brush the skewered caps with oil, and sprinkle with salt and pepper. Lightly oil the grill grates. Grill the skewered caps until the meat is browned around the edges and the mushrooms are charred and beginning to soften, 7 to 9 minutes per side.
Transfer the skewers to a serving platter, and garnish with the remaining parsley, Parmesan shavings and a squeeze of lemon. Serve with the lemon wedges.