Any bulky base will do: for example, t-butoxide.
Br- doesn't like H+ because it's big and quite stable with the negative on it (Think: it has a big house so e- can run around -> stable). This guy is best as anion.
Cl- is not as big (e- have less place to run around -> less stable with negative on), this guy will want to take up H+ more than Br-, but will be ok as anion.
F- is super small (e- have NO place to run around -> not stable). This guy is addicted to H+. This is the worse anion.
When something is stable, there's no reason for them to react, like Br-. When something is NOT stable, they will react right away like F-.
Do you remember why HF is a weak acid and HBr is a strong acid? This is why. Think simple: everything want to be stable, if they are not stable yet, they will react all they can to be stable.
Stability is the key.