Preheat the oven to 200°C (180°C fan).
Pat the Cornish game hens dry with kitchen paper. If you like, truss each with kitchen string.
In a small bowl, combine the softened butter, minced garlic, chopped rosemary, chopped thyme, salt and black pepper.
Gently loosen the skin over the breast and thigh of each hen and spread half of the herb butter mixture under the skin; rub the rest evenly over the outside of the hens.
Cut the lemon in half and place one half inside each hen’s cavity. Add a few sprigs of fresh rosemary and thyme, if you like.
Scatter the onion and carrots, if using, in the base of a roasting tin, then place the hens on top, breast-side up.
Roast for 40–50 minutes, until the skin is golden and the juices run clear when the thickest part of the thigh is pierced, or a meat thermometer inserted into the thigh reads 74°C.
Remove from the oven and rest the hens for 5–10 minutes before carving.
Serve with roast potatoes, green beans or a simple salad.