This build I made because I couldn't find an AP ezrael build I liked, so I made my own after many many games as AP ez. I find he is one of the most under-rated Mid lanes. And though it is true he is easily countered in the lane, he is one of the few mid champions that does absolutely fine without much farm, I sometimes have finished games 11/1 with fewer than 64 cs. The key is to play safe in the lane until you can burst a kill.
Also AP Ez is one of the most fun champions to play and takes quite alot of skill.

The Runes I run are a bit odd ball, I would recommend going full AP quints.

There are some circumstantial items, these items take the place of the hourglass at the end, if their team is building MR because of all the destruction you are causing, build a voidstaff. If you need a bit more mr, build a Holy grail early. I dont recommend guardian angel on ez because zhonyas helps you all the same except gives you that 100 AP.

Pros:

Great Burst
Great late game/mid game
Isn't reliant on farm
Great ganker
Great escapes/jukes

Cons:

Squishy
Not the greatest in lane
If stunned, easy kill

As ezrael if you are up against a long ranged poker like cass, it is better to not get the farm than to be poked, as well as laneing against morgana, if you get hit by her Q, you are as good as dead, it is better to not be hit by the Q than to lose a few minions.You should use your W as often as you can to hit them, try to bait their poke, then W them. Your E should be used strategically, it shoots a shot at the nearest enemy, creep or player. So after you dodge your opponents poke, it is a good idea to try to E near them, then W them, and fall back, This burst is amazing amounts of damage if done right and can lead to a kill within a few pokes.

E is one of the most poorly used skills I see on AP Ezraels. They assume because ez is so squishy it should be used for running, when in actuality, it can be used as a game breaker. E should be used often in lane, after the opponent uses a cooldown, E right next to them and W them, then fall back before cooldowns are back up. Later in the game E can be used to get over walls, often as Ezrael you do not want to initiate a team fight beacuse you are so squishy, you want to stay in the bushes and wait for the time to strike, an ult-E-W will kill any ap/ad carry and most supports immediately, The key with ezrael is dont get caught in a fight you cant win. One of the errors I see AP ez's do is use E to hop at somebody, W them then stay there trying to kill them, Ez is a burst champion after E W maybe Q if you have time, back off until a cooldown is back up It is worth it and will get you the kill.

The ult as ap is amazing damage, and what really sold me to AP ez. Late game the ult can get up to 1200 or more damage. It is not something to be thrown around. Mid game the ult should be used mainly for securing a kill at mid, but if mid is uneventful it is a great gank initiater or finisher, and alot of fun to gamble and try to snipe a straggler. But late game in team fights the ult is vital. It should be used as soon as it can hit all 5 champions, dont wait for the end to get the kills, wait until you can hit all 5 or 4 of the champions. It will completley change the fight around. Sometimes just the ult hitting everybody and bringing them to half health demoralizes them and makes them run away, making for easy pick offs.