Add egg to a large bowl and gently whisk. Add all remaining Hamburger ingredients and mix with your hands just until combined. Form mixture into 4 equal patties roughly the size of your hamburger buns. Refrigerate for 15 minutes.
Mix together the Hoisin ketchup, set aside.
Mix together the slaw ingredients, toss to combine, set aside.
Grill burgers for 4-5 minutes on each side or until desired doneness. If desired, toast buns on the grill too!
Assemble your burgers with hoisin ketchup and slaw and enjoy!