As Bob mentions, the ½” slab with a ¼” mirror is a common approach. The challenge here is the cup depth of the hinge. I think you would be Ok if you through-bore the ½” panel first, apply the mirror then install the hinges (carefully). In this case, almost any 110 degree free swinging hinge with an 11mm cup depth would be suitable.
If you want to stay with a ¾” substrate and the mirror then a thick door hinge would be required as most standard hinges, can accommodate a thickness of only about 22mm. As Jason mentioned, the 170 or 165 degree hinge would work if using a restriction clip. You should be able to find two types of restriction clips. One that stops the door at 110 degrees and another that stops the door at 125 degrees. A free swinging, 165 degree hinge should not be a problem to locate.
It has been my experience however that the full 165 degree opening is preferred for medicine cabinets. Most of the high end national manufacturers of medicine cabinets use a wide angle hinge. Some even apply a mirror to the back of the door as well. I think you will have a problem locating a “free swing” thick door 165 degree hinge however. Salice offers a thick door, 94 degree hinge in free swinging but not in the 165 degree hinge. (See page below).
I assume you are looking for free swinging hinges to use in conjunction with touch latches since there will be no handles on the mirror.
An alternate idea would be to consider the Salice thick door, 155 degree hinge with the “Push” to open feature. The movement of the Push hinge will open the door much further than a touch latch and permits a handle free surface on the door. The door is held closed by a small magnet. This is also a common technique used by the manufacturers of medicine cabinets with thicker doors and no handles. (See illustrations below). This Push hinge can accommodate doors up to 1-1/4” thick with very small gaps (3mm) between even the thickest of doors. This approach also eliminates the need for a touch latch which seldom work well over the long haul. Salice Push hinges and Blum hinges have the same boring pattern.
Are there more than 2 doors in your layout? Is it to be frame or frameless construction? Are the doors overlay or inset? The answers to these questions will also influence your choices.
Please forgive my lengthy reply here but I find this topic rather interesting due to the many possible solutions.
My 2 cents…