Preheat oven to 375˚F.
In a large mixing bowl, toss together the ground meats with onion, garlic, spices and parsley until combined. Score the meat into 4 equal portions then form patties.
Preheat a large, nonstick skillet with the EVOO and add the patties to the skillet. Add the burgers and cook for about 3-4 minutes per side.
While the burgers are cooking, heat up the sauerkraut in a small saucepot and reserve warm.
Place two pieces of cheddar onto each patty, then pop the skillet into the oven to melt the cheese, about 2-3 minutes.
Meanwhile, spread some grainy mustard on one side of all bread slices.