repair Dansk tray??  

The "best" way is to
separate the failed joint completely into two pieces and then prepare the surfaces to be re-joined by making them straight, flat, and clean before gluing and clamping.
The failure was most likely caused by the stresses of uneven seasonal movement and/or prolonged exposure to liquids or dry heat.

Thanks
what type/brand of glue would you recommend

For a teak cutting board?
I almost hate to say it because it can be tricky, but I'd probably use an epoxy. Depending on the amount of glue-surface contact area, though, Titebond type III might be okay, too. Some recommend wiping the surfaces of teak with acetone just prior to gluing to remove natural waxy resins that may interfere with proper adhesion.
I think for wooden cutting boards, keeping them oiled and drying them as quickly as possible after exposure to liquds is key to their longevity. Of course, quality of original construction is assumed with most vintage Dansk, though I've seen occasional QC problems now and then. Nobody's perfect, especially with the high-production runs.

Gorilla Glue
Ive done more than a few fixes on Dansk trays and pepper mills.
Gorilla Glue works the best. Lightly wet the joint and put in a minimal amount of glue. You wont need much. Use any flat tool/piece of paper and push the glue into the joint. Clamp the piece so that the joint becomes tight. Wait 5 minutes and wipe off glue which squeezes out of the joint. Repeat every few minutes until no more glue is coming out of the joint.
Leave overnight and un-clamp the following day.
Post an image and I can give more specific feedback. I would recommend the method above if you've never done something like this before.

thank you!!
for all the helpful information...