Specifically, I'm wondering if a Way of Shadow Monk can use Shadow Step, while being the controlling creature in a grapple, in order to move the target of the grapple.
Secondly, is the 60' range of Shadow Step affected by the halved speed caused by grappling?
In other words, can a Monk (1) run in, (2) grapple a creature, and (3) teleport away while bringing the creature with them.
It seems like it to me, but I'm somewhat unsure. These are some points I've considered:
The condition ends if an effect removes the grappled creature from the grappler ...
[..] as a bonus action, you can teleport up to 60 feet to an unoccupied space that you can see...
Moving a grappled creature: When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is 2 or more sizes smaller than you.