First cut the backbone out of each Cornish hen. Place the birds, breast-side down, on a chopping board and, using a sharp pair of kitchen scissors or shears, cut along either side of the bone to remove completely. Turn over and flatten the hens by pressing down with your hand over the breast bone.
Combine all the marinade ingredients and place in a large, resealable freezer bag with the hens. Seal the bag and leave to marinate in the fridge for about 24 hours.
When you’re ready to cook, preheat the oven to 400 degrees F (200C).
Take the birds out of the bag, reserving the marinade to make the sauce. Arrange them, breast-side up, in a large roasting tin and drizzle over the honey.
Place in the oven to roast for about 20 minutes. Measure the cornstarch into a small bowl, add the marinade and mix until smooth. Pour the marinade over the hens and return to the oven for a further 15 minutes.
Remove from the oven and cut each bird in half along the breast bone. Strain the juices left in the tin to make a sauce, seasoning with salt and pepper to taste. Serve half a hen per person, with some of the sauce spooned over.