Rotate non-forward vector to face direction?

This feels like it should be obvious but I've been walking myself in circles for ages.

I have a cube that moves by flipping, and when I click, I want the face that is closest to the target point to rotate to look at it. I can get the facing direction of the closest face easily, the trouble is that every rotation option I find assumes it's rotating the forward vector to look in the direction. Here's what I'm currently using:

 float step = speed * Time.deltaTime;
 Vector3 newDir = Vector3.RotateTowards(facing_direction, target_direction, step, 0.0F);
 cube.transform.rotation = Quaternion.LookRotation(newDir);

But LookRotation creates a rotation where the given vector is forward. Seeing as my forward could be facing any way, it's giving me the wrong result. I thought perhaps I just need to offset the rotation and tried adding:

 Quaternion offset = Quaternion.FromToRotation(facing, cube.transform.forward);
 cube.transform.rotation = Quaternion.LookRotation(newDir) * offset;

But it's still freaking out. Is there an easy way to do this?