2. Prepare the apricot sauce: Bring the water and sugar to a boil in a small saucepan over high heat to make a syrup. Remove from heat. Let cool.
3. Puree the apricots in a blender with half of the sugar syrup. Adjust the taste by adding a few drops of lemon juice and more sugar syrup until a pleasant balance of sweetness and tartness is reached. Divide the sauce in half and set aside.
4. Rinse the Cornish hens with cold water and pat dry. Season with salt and pepper inside and out.
5. Stuff the insides of the hens with garlic and thyme. Place a few pieces of shallots, carrots and celery in the cavity.
6. Scatter the rest of the shallots, carrots and celery on the bottom of a roasting pan. Place the hens on top of the vegetables.
7. Brush the hens with half of the sauce and roast in the oven until the the hens are golden brown and crisp and the juices run clear when the thigh is pierced with a sharp knife, about 45 minutes.
8. When the hens are finished, transfer them to a serving platter and let rest for about 5 minutes. Remove the skin from the hens and cut each one in half. Serve with the remaining apricot sauce.