Can't remove the handle on Moen shower handle... Seriously!!!

Moen posi-temp cartridge. 1222/1222B
-or-
Moen 96988 Cartridge Repair Kit Posi-Temp 1 Handle tub/shower

https://www.moen.com/shared/docs/exploded-parts-views/82000pt.pdf

Best to have the Moen Cartridge Puller.

http://pro.moen.com/1-handle-replacement-cartridge-posi-temp/_/R-TPORTAL-ALL%3A1222B

defective part

It may be but it would depend on how and why it broke. If the unit is less then a year old Moen is always pretty good about replacing parts.
I can't give you a ferm amount on replacement not knowing witch handle you have but they range from $6 to $150 depending on the handle and the finish. The link below will give you good idea.

http://www.moen.com/replacement-parts

Remove the handle and see if it will turn off without the handle and if it will reposition the handle alignment and your good to go. If no the cartridge will need to be replaced.

How I remove them is take a drywall screw and screw in to the flow restrictor. Then grab it with a pair of pliers and pull out.

If your Posi-Temp has no water coming through the valve my first step would to replace the cartridge (Moen pn 1222). The valve as a simple one. Get the part first so you can ues the plastic tool that comes with it if you need to. Beneath the actual lever insert on the handle hub you will notice a small hole. this is to gain access to the allen head screw which holds the handle in place

You have to remove cartridge and rotate 180 degrees then re-install. Was it removed or replace lately?

turn the water off to the shower,sometimes you must shut down the whole house at the main ,near the water meter,then take the handle off slide the clip in front up and out then pull posi-temp straight out.replace posi-temp in reverse order.be mindful of the H/C indicator on posi-temp this will ensure you have hot and cold on right sides,if reversed just flip posi-temp.

I hate to say this but maybe the inside of the allen screw has been rounded out by a previous worker. You can drill the screw out and replace the handle with a new one. NOTE: Moen replacement parts are not cheap!

Is this only happening in your shower? Or through the hole house? Maybe you shower head has a flow restrictor in it. Try removing it!