Combine the ketchup, mustard, honey, and cayenne in a small bowl. Cover and set aside.
Heat the olive oil in a large skillet on medium heat. Add the chopped beef and cook until no longer pink, stirring 5-7 minutes. Strain beef, discarding liquid, and return to skillet. Reduce the heat to medium low and stir in cheeses. Cook until cheeses melt, 2-3 minutes. Season with salt and pepper to taste. Set aside to cool.
Place 1 wrapper on a clean work surface, keeping the other wrappers covered with plastic wrap. Brush the entire surface of wrapper with egg yolk. Form 1/4 of the beef mixture into an 8" log along one edge of the wrapper. Roll up the wrapper, leaving ends open. Place a second wrapper on the work surface with a corner facing you, brush the corners with egg yolk, and lay the first roll across the bottom corner of the second wrapper. Roll up wrapper, tightly folding the ends over halfway through. Press down slightly to seal and set aside. Repeat the process with remaining wrappers and filling.
Pour vegetable oil into a heavy medium pan to a depth of 2" and heat over medium heat until the temperature shows 350°F on a candy thermometer (You don't have to have a thermometer, just make sure the oil is hot, but not smoking). Fry spring rolls in 2 batches, turning over halfway through, until golden brown, about 8 minutes. Cut into thirds on the bias and serve with sauce. Good with pickles on the side. Enjoy!