Defrost the cornish hen. Cornish hens are usually frozen. Defrost in the fridge overnight. Make sure to add a plate underneath to catch any liquid as it defrosts.
Prep the sweet rice. Add the sweet rice to a medium bowl. Rinse with water and drain until the water is no longer cloudy, about 2-3 times. Add enough water to cover the rice about 1/2 inch. Set aside to soak for 30 minutes.
Stuff chicken. Rinse off the cornish hen with water, as it can get quite bloody from the defrosting process. Salt the inside cavity of the chicken. Stuff the chicken by adding 1 jujube and the pre-soaked sweet rice into the cavity. Tie the chicken legs together with kitchen twine so it will hold the sweet rice in place. Alternately, use a small, sharp knife and cut a slit into the chicken skin near the opening of the cavity. Slide the chicken leg on the opposite side into the hole. Tuck the remaining chicken leg into the space between the secured leg and the chicken body. Sprinkle the chicken with salt, all over.
Cook in the Instant Pot. Carefully place the stuffed chicken to the inner pot of the Instant Pot. Add cold water, ginseng root, remaining jujube, garlic cloves, and chicken bouillon. If using, add additional medicinal herbs (milk vetch root, ginkgo nut, and chestnut, etc.). Lock lid into place and make sure the vent is in the "sealed" position. Turn off the "Keep Warm" function. Pressure cook for 14 minutes. When it finishes cooking, Natural Release for 10 minutes. Release any remaining steam and unlock the lid.
Cook on the Stovetop. Carefully place the stuffed chicken to a large stock pot. Add cold water, ginseng root, remaining jujube, garlic cloves, and chicken bouillon. If using, add additional medicinal herbs (milk vetch root, ginkgo nut, chestnut, etc.). Heat over medium-high heat until boiling. Skim off the fat and scum as it bubbles to the surface. Lower heat to medium and cook (covered) until the chicken is cooked through, about 30 minutes. Lower heat to medium-low and simmer (covered) for another 15-20 minutes until the chicken is very tender. *Add more water if the liquid evaporates too quickly.
Transfer to a serving bowl. Using tongs and a large spatula (to hold the bottom), transfer the cornish hen to a large, preheated serving bowl. Remove the jujube and ginseng root and add to the bowl as well. Finally, add the chicken broth.
Optional: Use a fine mesh sieve to catch any debris from the cooking process as you pour the broth into a bowl. It will make for a clearer broth.
Serve. Garnish with green onion and cracked black pepper. Serve with white rice, kimchi, and more green onion. Also, serve a small bowl filled with salt and black pepper for each person. That way, people can season their soup or dip chicken pieces into the salt and pepper mixture. Enjoy!