Rinse and dry two Cornish game hens with paper towels. Rinsing the product removes any naturally occurring moisture released from the hens while they're packaged, and drying it thoroughly facilitates a process known as Maillard reaction. When a protein is exposed to heat, a complex chemical shift takes place that causes amino acids to take on the properties of a simple sugar that caramelizes.
Dice an onion and two large carrots into pieces approximately 1 to 1 1/2 inches in size. The dimensions of the vegetable cuts are not as important as their uniformity for consistent cooking.
Remove any extraneous pieces of fat hanging from the hen, and lightly coat the product's surface with olive oil. Season the hens liberally with kosher salt and freshly ground black pepper, including inside the cavity. Insert fresh aromatic herbs into the cavity with two garlic cloves.
Place the hens, 1/4 cup braising liquid and vegetables into the slow cooker, secure the lid and set the temperature to "Low." Approximately two hours into the cooking process, evenly disperse the vegetables along the bottom of the cooking vessel, and set the hens on top. This allows air to circulate beneath the product while cooking and facilitates even heat distribution.
Check the internal temperature of the hens using a meat thermometer approximately four hours into cooking. When the hens reach 150 degrees F, remove them from the slow cooker, tent them with foil and allow them to rest a minimum of 20 minutes. Do not break or pierce the surface of the product while resting. Meat undergoes a process referred to as carryover cooking upon removal from a heat source, which brings the product to a safe internal temperature of 165 degrees F. While resting, proteins reabsorb the naturally occurring moisture released during cooking, yielding a moist final product. Cooking takes approximately five to six hours, depending on the size of the hens.