Let stand for 20-25 minutes, then discard towels and brush off excess salt. Drain hens and shallots from marinade. Strain marinade into bowl and place near grill with brush for cooking. Save bay leaves from marinade. Season hens and shallots with salt.
Place hens, skin-side down, on grill.
Tuck bay leaves under hens and cook for 12-15 minutes. Brush inside of hens with marinade as they grill. Cook for another 12-15 minutes. Do not brush with marinade during last 5 minutes of grilling. Hens are ready when flesh is no longer springy and, when lifted, juices run clear and internal temperature is about 160 degrees.