Remove outer leaves from brussels sprouts. Cut off bottom stem and slice each sprout in half long ways. Rub with olive oil and season lightly with salt and pepper (about 1/4 tsp. each). Roast for 30 - 35 minutes.
While brussels sprouts are roasting, heat butter in a sauce pan over low heat while whisking for 5 - 10 minutes until butter starts to brown and smell toasty. Be careful not to burn the butter! If it burns, you will have to throw it out and start over which is why low heat is necessary.
Once butter is browned, add soy sauce and balsamic vinegar and whisk to mix in. Remove sauce from heat. Toss brussels sprouts in sauce and season with salt and pepper to taste before serving.