Pound the cardamom pods to loosen the husks. Use a mortar and pestle to pound the seeds, releasing their flavor. Add the garlic, salt, and oregano; and continue to pound until the ingredients are well mixed.
Add 3 tablespoons of olive oil, and continue to crush until you have a smooth paste.
Rub 3/4 of the paste over the hens, making sure you cover all of their surfaces.
Mix the remaining paste with the remaining olive oil, and pour over the birds, reserving a little bit to baste with while grilling.
Cover and marinate for at least four and up to eight hours, turning occasionally.
Preheat a grill to high.
Season the birds with plenty of pepper, then place on the grill and sear being careful of flare-ups, until the skin is golden.
Move the birds to indirect heat, and grill until completely cooked, basting with the reserved marinate during the last few minutes of cooking.