Make the fried cheese: Pulse the provolone and parmesan in a food processor until the cheese gathers into a ball; transfer to a bowl. Pulse the yellow cheddar and 2 teaspoons flour in the food processor until smooth. Form teaspoonfuls of the yellow cheddar mixture into 12 small balls; roll between your hands until smooth. Transfer to a plate and freeze until firm, about 15 minutes.
Wipe out the food processor. Add the pretzels and pulse until finely ground with a few chunks; transfer to a shallow dish. Mix the remaining 1 1/2 cups flour and 1/2 teaspoon pepper in another dish. Whisk the eggs and mustard in a third dish.
Roll tablespoonfuls of the provolone mixture into 12 balls, then flatten into disks. Put 1 yellow cheddar ball on each disk, then shape the provolone around it, enclosing the cheddar. Roll into an egg shape.
Dip the cheese balls in the egg mixture, then dredge in the flour; return to the egg mixture, then roll in the pretzel crumbs, turning to coat. Refrigerate at least 20 minutes and up to 3 hours to set the coating.
Preheat the oven to 350 degrees F. Heat 1/2 inch peanut oil in a saucepan until a deep-fry thermometer registers 360 degrees F. Fry the cheese balls in batches, turning, until golden, 30 seconds to 1 minute. Remove with a slotted spoon and transfer to a rack set in a baking dish. Bake until heated through, 5 to 7 minutes.
Make the sauce: Whisk the horseradish, mustard and sour cream in a bowl. Serve with the fried cheese.