Preheat oven to 375F.
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.
To serve, place all the burgers onto four slices of bread then divide the sauerkraut amongst the burgers and top with the remaining slices of bread.