Brownies are a monster that is generally best left ignored. They are always generated asleep, like all nymphs, and so can be safely left alone. When awoken, they are fast spellcasters who are quite often able to cast spells such as destroy armor and curse items, to say nothing of their ability to steal your items and then teleport away. They also have many more hit dice than the typical nymph, having a base level of 8 instead of 3. It is well worth checking if that n is a mountain nymph or a brownie, as the brownie is truly best left alone.
If you do find yourself confronting a brownie that is awake, the best strategy is to use ranged weapons and/or Elbereth. They are not a great threat, particularly since they only have one theft attack. They are just not worth the trouble to kill, since they can be left alone, and killing them entails the risk of having your items cursed or stolen.