Season the grouse or pheasant inside and out with salt, pepper, minced garlic, and chopped fresh rosemary.
Tuck wings under body. Heat a heavy-duty skillet over high heat until smoking hot (you can add oil for extra flavor). Add grouse or pheasant breast side down and sear quickly to build browned crust on the outside, about 1 minute per piece.
Turn breasts with tongs. Grill skin-side up just until golden brown but not burnt (another one to two minutes), basting occasionally with remaining rosemary sprigs soaked in olive oil during grilling time.