I agree with what was said above. Brown sugar is simply white sugar with molasses. Molasses will ferment out to a rum-like flavor, but there's not very much molasses in brown sugar, so you probably won't be able to pick it out anyways. The sugar itself will pretty much ferment out to ethanol.
In other words, by addling the brown sugar you just added about 12oz of everclear and maybe a shot glass of 151 to your batch (assuming 2kg brown sugar in a 5gal batch).
Like they said above, if you are looking for more complexity/depth and also body/mouthfeel, add some dark crystal (like Crystal 90-120) and more base malts. If you are using extract, just use more DME and maybe add a bit of amber extract and maybe steep in a touch of chocolate malt (just a few oz). A cup of maltodextrin powder can aid the body, too, without sweetening up the beer.