Set a rack in the center of the oven and heat the oven to 450 degrees F. With a sharp knife or poultry shears, remove the backbones from the hens and slice through the breastbone, cutting the hens in half. Brush the skin of the hens with 2 teaspoons of the sesame oil and set them, skin side up, on a wire rack set in a rimmed baking sheet. Sprinkle the skin with 1/2 teaspoon salt and several grinds of pepper. Roast until the hens are almost cooked through (an instant-read thermometer inserted in the thickest part of the thigh should register 165 degrees F), about 25 minutes.

Meanwhile, heat the remaining 2 teaspoons sesame oil in a small saucepan over medium heat. Add the ginger and garlic and cook, stirring often, until soft and fragrant, 2 to 3 minutes. Stir in the preserves, honey, soy sauce, and lemon juice; bring to a boil and cook, stirring occasionally, until the mixture has thickened slightly, 4 to 5 minutes. Dissolve the cornstarch in 1 teaspoon water, add to the saucepan, and cook until the mixture thickens, another 1 minute.

Brush the hens with the apricot-ginger glaze and continue to roast until the glaze has browned in spots and the thermometer registers 170 degrees F in the thigh another 5 to 7 minutes. Season to taste with salt and pepper and serve immediately.

Serving Suggestions: Serve with a basmati rice and scallion pilaf and a baby spinach salad.