so last year I covered open space in the garden with alfalfa,

seems like a good cover crop, nitrogen building, covered much of my open garden space here in MD. worked quite well till winter hit

frost/freeze was supposed to kill the stuff, I've already got it growing like a weed in many of the same spots even after several tillings.

not sure what to do, suggestions to get rid of it, or keep it since it's a good nitrogen producer? could let it grow as a living mulch? from what i've dug up (planted potatoes this past weekend), it's got deep medium heavy roots.

I don't want it to turn into another garden weed, so what should I do?