CharacterController slides on borders of cubes

I’m trying to create a Minecraft clone and I’m using Unity’s FPSController, which has a Character Controller which is made of a vertical capsule.
The problem is that when you are standing in top of a block, when you approach the border and fall, it doesn’t quite act like Minecraft.

For example: this gif represents what happens in Minecraft (CH represents the character):

Where as with Unity’s Character Controller this is what happens:

So there’s a bit of a “sink” when approaching the border. I don’t want this.

So my question is: how do I make my character to collide against other cubes as a cube, but retain the ability to walk on slopes as a vertical capsule.?

i think its not so much a controller problem but more a rigid body problem. I believe if you increase the gravity on your player and increase the jump height in the controller(so that he still jumps the same height) that should fix this sliding issue(not entirely sure what you mean by sliding).