Preheat the oven to 350 degrees.
Prepare the sprouts by cutting of the stem and finely cutting them crosswise into 1/8 inch shreds. In a small mixing bowl toss the shredded sprouts with the garlic, olive oil and salt and pepper until coated well.
In a small sauce pan over medium-high heat add the balsamic vinegar and bring to a boil. Lower temperature to low and simmer until reduced about half way. Take off heat. It will thicken as it cools.
Preheat an iron skillet to medium low. Cut the guanciale into 1/8 inch cubes and once the skillet is warmed up toss the guanciale in until it renders off the fat. About 5 minutes. Remove and drain on paper towels. Keep the fat in the pan.
Put the brussel sprouts in an oven safe pan, uncovered, then in the oven on the center rack for 20-25 minutes stirring halfway through.
When the sprouts are about halfway done turn a burner on medium-high and put the iron skillet with the fat in it back on the burner. Sprinkle a little salt and fresh ground pepper on one side of the pork chop. When the oil gets hot and is beginning to smoke add the pork chop, salt, and pepper side down. Sear for about 5 minutes until it's nicely browned. Pepper and salt the top side then flip it over.
The Brussel sprouts should be done by now so remove them from the oven and put the iron skillet with the chop in on the middle oven rack and cook for another 10-15 minutes or until the center of the pork chop reaches about 110-125 degrees or hot enough to eat. Sprinkle a little grated Parmesan on the sprouts and add the guanciale to it. Heat it back up as needed on the warm burner. Drizzle the balsamic vinegar in a cool design on the plate. Top with the chop and the Brussel sprouts, serve right away.