Preheat oven to 450 degrees F and place cast iron skillet inside to heat.
Rinse and pat dry cornish hens. Salt the hens 15 minutes before cooking to draw moisture out. Pat dry again.
Combine finely chopped herbs (reserve 1 tsp of rosemary) and butter. Season with salt and pepper.
Carefully slide your fingers under the skin of each breast (from the butt-end of the bird) to create 2 'pockets' between the skin and meat. Rub 2/3 of the herbed butter into these pockets. Season the hens generously with salt and pepper.
Melt remaining compound butter and combine with maple syrup to create the basting liquid.
Toss potatoes in oil and remaining rosemary.
Carefully remove hot skillet from oven and oil the bottom. Place Cornish hens in skillet, breast-side up, and add potatoes, onions and garlic around them.
Brush melted compound butter onto hens and place skillet back in oven. Be sure to brush the entire bird.
Halfway through cooking time, add carrots to pan with potatoes and onion. Baste hens with the remaining maple-butter mixture.
Continue to cook cornish hens until a thermometer placed in the meatiest part of the thigh reads a temperature of 165 degrees F; 45 - 55 minutes. Remove from the skillet, loosely cover with foil and allow to rest for 10 minutes before serving.