Slice or shave brussels sprouts very thin and slice the jalapeño into thin rounds, set aside.   Set 2 to 3 cups of water to boil in a kettle or a sauce pan.  In a container with a lid, like a mason jar, add vinegar and sugar.  Stir to combine.

Place the sliced sprouts and jalapeño in a colander.  Once the water is boiling, pour slowly over the cabbage until all the water is gone.  This can be done over the sink or over a large bowl.

Transfer the hot sprouts and jalapeños to the container with the vinegar mixture.  Let sit for 30 minutes before using.  Flavor will develop and the harshness of the vinegar will mellow the longer it sits.  Store covered in the refrigerator up to 3 days.

Separate the lamb into 6 even sections, a little over 5 ounces each.  Remove about ⅓ of the meat from one section and flatten into a disk.  Repeat with the remaining half of the section so you have two lamb patties, one smaller than the other.  The easiest way to flatten the lamb into patties is to place it in between parchment paper or plastic wrap and press it this with something heavy - like a cast iron pan or sauté pan.

Layer slices of feta on top of the larger patty.  Top with the smaller patty and fold the ends over to seal in the cheese.  Smooth out any gaps so the cheese doesn't escape during cooking.  Repeat for the remaining ground lamb.

Season eat side of the burger with salt and pepper.  Grill or pan fry for 5 to 6 minutes per side.  You want the lamb to be cooked to 160°F, about med well and the center to get hot enough for melty cheese.  Let the cooked stuffed lamb burgers rest for 2 minutes while assembling the toppings for your burgers.

Layer each bun with Brussels sprout and jalapeño slaw, juicy feta stuffed lamb burger, then top with creamy tzatziki sauce.