Line a baking sheet with a layer of paper towels for draining. Into a Dutch oven, pour about 1½ inches of oil and heat the oil to 400°F over medium heat.
Put half the Brussels sprouts and any leaves that have fallen off into the hot oil. Turn the heat up to medium-high and cook for 3 to 5 minutes, stirring them often until they are dark golden brown and crisp. Remove with a slotted spoon to the prepared baking sheet to drain. Immediately season with ¼ teaspoon of salt.
Bring the oil back up to temperature, add the remaining Brussels sprouts to the oil and repeat step 2.
Place the crispy sprouts on a serving plate, sprinkle with the Parmesan cheese, and drizzle with the balsamic glaze. Serve immediately.
NOTE: Emilie says that to ensure that the sprouts come out crispy, and to reduce any splattering, make sure that they are dry and at room temperature prior to frying. Don't use frozen sprouts, since they have much more moisture. Use a screen to control the splattering but don't use a lid, which will make the splattering worse.
