In a large bowl, mix the yogurt, ginger, garlic, tandoori masala, and 1/2 teaspoon salt.
Rinse hens and pat dry. Using poultry shears or a sharp knife, cut hens in half through breastbones and backbones. Turn birds skin side up and press with the palm of your hand to flatten; a few bones will crack.
Turn birds in yogurt mixture to coat. Cover and chill at least 30 minutes or up to 1 day.
To barbecue over charcoal, ignite 60 briquets on firegrate in a barbecue with a lid. When coals are spotted with gray ash, in 20 to 30 minutes, bank about half the coals on each side of the firegrate. Place a drip pan in the center. Set grill above coals.
To barbecue over gas, turn gas barbecue to high heat and cover for 10 minutes. Adjust for indirect heat.
Set hen halves about 1/2 inch apart on center of grill, not over heat. Cover and cook until meat is no longer pink at thigh bone (cut to test), 30 to 35 minutes total.