If using wooden skewers, soak them in water for at least 1 hour prior to cooking.
Trim off the ends of the Brussels sprouts and remove any outer brown leaves. Place in a large mixing bowl and microwave on high for 3 minutes (if you do not have a microwave, instead blanch the Brussels sprouts in boiling water for 3 minutes then plunge them into an ice bath. Dry well before proceeding.). Let cool.
Preheat an outdoor grill to medium heat (about 375 degrees F). You also can cook these Brussels sprouts on a grill pan on the stove or broil them in the oven. See blog post above for suggestions.
When the Brussels sprouts are cool enough to handle safely, using the same bowl, top them with the olive oil, garlic, soy sauce, balsamic, mustard, salt, and pepper. Toss to evenly combine.
Assemble the skewers: Thread 4 to 5 Brussels sprouts onto each skewer with the stem ends facing in the same direction. Leave at least 1/2-inch in between each sprout. If your Brussels sprouts are mixed in sizes, group ones of similar size on the same skewers so that you can cook them evenly. Reserve the remaining soy sauce balsamic mixture in the bottom of the bowl (it's tasty and we'll use it again).
Place the skewers onto the grill. Cover and let cook for 5 minutes. Carefully turn the skewers over. Recover the grill and continue to cook for 5 additional minutes, until nicely browned and you can easily pierce them with a sharp knife.
Carefully remove the Brussels sprouts from the skewers, returning them to the bowl with the reserved soy sauce balsamic mixture. With a large spoon, stir to coat. Then transfer to a serving plate or serve directly from the bowl. Enjoy!
TO STORE: Refrigerate Brussels sprouts in an airtight storage container for up to 3 days.
TO REHEAT: Rewarm leftovers on a baking sheet in the oven at 350 degrees F or in the microwave.
TO FREEZE: I do not recommend freezing cooked Brussels sprouts, as they will be quite mushy once thawed. However, you can freeze Brussels sprouts if needed. Freeze them in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.