Use a large sauté pan and place over medium-high heat. To this, add the oil and bring up to temperature for 1 ½ minutes.
Add some of the Brussels sprouts, some of the garlic and pinch of salt. I do this in two big batches, but adjust to the size of the pan you are using. Also adjust the amounts of lemon zest, lemon juice, and parmesan you use in the next step. How much you use is not critical. You just want each batch to be evenly seasoned.
Use a set of tongs or kitchen spoon and toss the Brussels sprouts, moving them around as they sauté. Be mindful to brown and not burn the sprouts by turning them often. Once the sprouts are cooked, add the ½ lemon zest, ½ lemon juice, ⅓ parmesan and toasted pine nuts (optional). Toss to mix thoroughly, then remove from heat onto the serving dish and keep warm. Repeat until all the sprouts have been cooked. Add the just-cooked sprouts to the reserved batch(es) and keep warm.
Serve the shaved Brussels sprouts as you need with the main course. These will keep well wrapped with a little alumunium foil in a warm oven. Right before service, drizzle with a little balsamic syrup and a little more cheese and serve.