Country Apple Fritter Bread

Name: Country Apple Fritter Bread
Cuisine: American
Ingredients: 1 cup milk (of choice); 4 tablespoons butter; 0.25-ounce packaged active dry yeast (about 2 ¼ teaspoons); 5 tablespoons granulated sugar; 1 ½ teaspoons coarse salt; 1 large egg; 3 ¼ cups flour* + more for dusting; 2 tablespoons butter; 3-4 medium firm apples, skins on, diced (about 4 cups); Juice of ½ medium lemon (about 2 tablespoons); 3 tablespoons brown sugar; 1 tablespoon ground cinnamon; Pinch coarse salt; ½ cup chopped walnuts (optional); ¼ cup powdered sugar; 1 tablespoon milk (of choice)