Heat the oil in a large skillet over medium heat. Prick the sausages with a fork, place in skillet, and cook, turning, until golden brown and cooked through, about 20 minutes. Remove and keep warm in a 200° F oven. Pour off all but about 2 tablespoons of the fat. Add the tomatoes, salt, and pepper. Sprinkle on the parsley and toss well. Cook until the tomatoes start to soften, about 5 minutes. Serve with Hash Browns.