Hi! Some peonies make great cut flowers, lasting a week in a vase, and some don't last long at all. You have to cut them when they are at what is called the marshmallow stage. That is when the flower is closed but slightly soft. I understand they can be refrigerated at that stage for up to six months. However, I've read people having trouble keeping peonies refrigerated for very long. Someone else will have to relate their experiences as I haven't tried refrigerating peonies.
One and done - yes. The buds can be seen as the plant emerges from the ground, and those are all it will make.