In a large bowl mix together the chorizo meat with the grated cheddar cheese. Use your hands to knead the chorizo mixture until the cheese is mixed through the meat.
Shape the chorizo mixture into 4 - 5 burgers and place them on smoker racks. Make sure the burgers are not touching.
Start up the smoker, using wood of choice (hickory or whiskey oak works very well!). Bring the smoker up to a temperature of 250F.
Place the burgers in the smoker and cook until the internal temperature reaches 165F.
Serve on a burger bun with toppings and condiments of choice.