Set a rack in the center of the oven and heat the oven to 450°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 ½ teaspoon salt and several grinds of pepper.
Roast until the hens are almost cooked through (an instant-read thermometer inserted into the thickest part of the thigh should register 165°F), about 25 minutes.
PREPARE THE SAUCE:
Heat 2 teaspoons of 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/jam, 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 of 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°F. in the thigh, another 5 to 7 minutes.
Season with salt and pepper, and serve immediately.
Notes
If you are preparing this recipe as GLUTEN-FREE, just be sure to use brands of apricot jam and soy sauce that are known to be GF.