Clean all the Brussels sprouts and make one cut from the top down toward the stem end, being careful not to cut all the way through. Make another cut crossing the first like an X also down toward the stem end but not all the way through. Set aside in a bowl.
Add the olive oil and pancetta to a large saute pan over medium heat. Crisp the pancetta just until it starts to brown, about 5 minutes, then remove it from the pan and drain off half of the fat in the pan.
Place the pan back on the stove over medium-high heat. Add the shallots and garlic and saute until translucent, about 3 minutes, then place the pancetta back in the pan as well.
Deglaze with the balsamic vinegar and reduce by half, about 5 minutes.
Add the chicken stock and reduce until you have about 1/3 cup liquid glaze in the pan, about 15 minutes.
Deep fry the Brussels sprouts until they are golden brown and green in color, 3 to 5 minutes. Drain on a paper towel-lined sheet tray, then toss in the pan with the glaze and stir well to coat.
Spoon into a serving dish and use a rasp grater to grate lemon zest and Parmesan over the top.