Why is there cracked paint on my new plaster?
The cracking would imply a drying problem. I would think that the cornice was primed improperly. If the primer was of cheap quality or the painter used a paint with a built in primer for drywall. The primer may have not effectively sealed the plaster. Then the drying of the paint would be effected, basically the plaster sucking out the moisture to quickly. this could cause the paint shrink and crack as it dried. 

Answer to comment.

You have to fill the cracks. either by sanding them out or filling them. If sanding isn't an option try coating an area with a light coat of mud and after it drys lightly wipe it smooth with a damp cloth. Then repaint starting with a good sealer, kiltz would probably do.

A type of self leveling paint might work without all the mud filling, but It depends on the size of the cracks. I would sample a couple areas to see what works best.

There are paints that claim to have this ability. I would still start with a good primer/sealer before anything.

Cashmere 

This is not an endorsement of the paint only an example of what to look for. I have never used it.