In a small saucepan over medium heat, melt the butter. Add the onion and sauté until soft and translucent, about 5 minutes. Add the flour and stir to form a paste. Pour in the milk and broth, whisking constantly until no lumps remain. Continue to cook until the mixture is smooth and thick, about 1-2 minutes. Transfer the mixture to a large bowl to cool slightly.
Add the egg, apple, lemon juice, chives, one of the raw eggs, salt, and freshly ground black pepper to the cooled flour mixture. Chill for 30 minutes.
Meanwhile, place the remaining two eggs in a shallow bowl; beat to combine. Place the panko crumbs in another shallow bowl.
Using a small ice cream scoop or spoon, shape the chilled egg/onion/apple mixture into 1-inch balls. Coat each ball in the beaten raw eggs, shaking off the excess, and roll them in the panko. Transfer to a rimmed baking sheet lined with parchment or wax paper. Chill the croquettes, loosely covered, for 1 hour.
In a deep fryer or heavy-bottomed deep skillet, heat 2-3 inches of oil to 350ºF. Using a bamboo skimmer/strainer, carefully lower a few croquettes into the hot oil. Fry, turning once, until the croquettes are golden brown, about 2 minutes.Transfer the croquettes to a paper towel lined baking sheet to drain. Continue with the remaining croquettes. Croquettes can be kept in a 200ºF oven until ready to serve.
In a small bowl, stir together the applesauce and horseradish. Serve the croquettes warm with the sauce. Enjoy!