Preheat the oven to 400°F (205°C).
Pat 2 Cornish game hens dry with paper towels; optionally truss each with kitchen twine.
In a small bowl, combine 2 tablespoons unsalted butter, 2 cloves minced garlic, 1 tablespoon chopped fresh rosemary, 1 tablespoon chopped fresh thyme, 1 teaspoon salt, and ½ teaspoon black pepper.
Gently loosen the skin over the breast and thigh of each hen and spread half the herb butter mixture under the skin; rub the remaining mixture evenly over the outside of each hen.
Cut 1 lemon in half and place one half inside the cavity of each hen; add a few fresh rosemary sprigs and fresh thyme sprigs if desired.
If using, chop 1 small onion into large chunks and chop a few carrots into large chunks; scatter them in the bottom of a roasting pan to create a bed.
Place the prepared hens breast-side up on the vegetables (if using) and roast in the preheated oven for 40–50 minutes, until the skin is golden and a meat thermometer inserted into the thickest part of the thigh reads 165°F (74°C).
Remove the pan from the oven and let the hens rest for 5–10 minutes before carving or serving.
Serve with your choice of side dishes such as roasted potatoes, green beans, or a simple salad.