Place sun-dried tomatoes in medium bowl. Pour enough boiling water over to cover. Let stand until softened, about 15 minutes. Drain. Saute sausages in heavy medium skillet over medium heat until cooked through, breaking up with back of spoon, about 5 minutes. Using slotted spoon, transfer sausage to paper towels and drain well. Butter 13x9x2-inch glass baking dish. Whisk milk, eggs, thyme, salt and pepper in large bowl to blend. Add sun-dried tomatoes, sausage, bread, onion and Parmesan cheese and stir to blend. Transfer to prepared dish. Cover and refrigerate at least 4 hours or overnight. Preheat oven to 375°F. Bake strata uncovered until puffed and golden brown, about 45 minutes. Sprinkle with mozzarella and goat cheese and bake until mozzarella melts, about 5 minutes. Transfer pan to rack and cool 5 minutes. Sprinkle with parsley.