Place hazelnuts on a baking sheet. Bake at 350° for 15 minutes, stirring once. Turn nuts out onto a towel. Roll up towel; rub off skins. Coarsely chop nuts; set aside.
Combine milk and next 7 ingredients (milk through egg) in a bowl. Add bread cubes; toss to coat. Let stand 15 minutes. Place a large nonstick skillet coated with cooking spray over medium heat until hot. Add quince; sauté 3 minutes. Add apple cider; reduce heat, and simmer 15 minutes or until liquid almost evaporates. Add quince, cranberries, and hazelnuts to bread mixture; toss gently to coat. Spoon into an 8-inch square baking dish coated with cooking spray. Bake at 350° for 35 minutes or until set. Let stand 5 minutes before serving.