Since Broww only lets you draw 1 card if you discarded it with your own card effects, you will need Ceruli to be Special Summoned to your opponent’s field, and then use Ceruli’s effect to discard this card to the Graveyard, to trigger its effect. Also note that Broww’s effect can also be activated during Damage Step if it was discarded to the Graveyard.
These are the cards that has effects of discarding cards from your hand to the graveyard. This concept is different than discarding cards as a cost to trigger the card effect. Dark World Lightning has effects that discards 1 card from your hand. Into the Void’s effect will discard your entire hand during your End Phase, so if you discarded all your Dark World monsters, you can trigger their effects. Dragged down to the Grave has mandatory effects for both players to choose 1 card from each other’s hand and discard it, and draw 1 card. Trance Archfiend’s effect allows you to discard 1 Fiend-type monster once per turn, to boost its ATK by 500 for that urn.
I haven't tested this card yet, but another Dark World card that involved an effect upon discarding didn't work with anything that wasn't another dark world effect, it didn't work with traps, or spells, or monsters that required discarding...
The card needs to be discarded by an effect, not cost. The difference makes no sense to me, but basically only Trance Archfiend,
Dark World Lightning, Into the Void, Dragged Down into the Grave work, or Ceruli, Guru of Dark World for discarding it.