[DJ Sensei]

Well the first thing to consider is that you're being laid 3.5-1 pot odds, which is sufficient to call even if you're dominated by AJ or 77 or some such hand. As a big stack here, with the power to bust the shorty (and become the overall big stack with even more power), a call is definitely in order.

If the button has been known to steal blinds often with minraises, an argument could be made for reraising to put him all in preflop, but i think with his stack that short, and your hand somewhat weak, its not a good idea.

So assuming you call (which IMO is the best play) and the flop has either a J or 7 and is safe otherwise (the only thing i'd be concerned about is a flop with 2 higher broadway), you can probably bust him out or take down the pot, leaving him in even more trouble.

Another thing to consider is the skill level of the button. A good player here, with any kind of a hand (or maybe no hand at all) would raise all in to take the blinds or maybe double up. In this case, a minraise might be a very strong hand which wants some action, in which case a fold isnt a bad idea (Even though the pot odds are still there or close to it if he's doing that with AA,KK,QQ,AK)

Against a fish, however, a minraise is more a weak attempt to steal the blinds. With any hand after the flop, you should be able to take it down.