Apple and Beer Cheese Soup

Name: Apple and Beer Cheese Soup
Cuisine: American
Ingredients: 5 tablespoons salted butter, divided; 1 cup chopped sweet onion; ½ cup chopped carrot; 1½ cups chopped peeled Granny Smith apple; ½ teaspoon kosher salt; ½ teaspoon ground black pepper; ¼ teaspoon dry mustard; ¼ teaspoon ground red pepper; 1 garlic clove, minced; ¼ cup all-purpose flour; 1 (12-ounce) bottle IPA beer; 1 cup chicken stock; 1 cup whole milk; 6 ounces shredded sharp Cheddar cheese; 4 ounces shredded smoked Gouda; 1 cup cubed marbled rye bread; ½ cup chopped pecans, toasted