For the herb gremolata:
- Preheat grill (or oven) to 500 degrees. Spatchcock the hen by laying it breast side down. Using kitchen shears, cut along each side of the backbone from thigh end to the neck and remove backbone. Flip bird over, opening it up, and press firmly on the breastbone to flatten. Season with olive oil, salt, and pepper. Tuck wing tips under breast to prevent burning.
- Season vegetables with olive oil, salt, and pepper, and place in a single layer on a roasting or cast-iron pan. Place hen on top of vegetables, skin-side up. Roast on grill or in oven until the thickest part of the thigh reads 165 degrees, about 15 to 20 minutes. If using a grill, remove bird and flip skin-side down for 1 to 2 minutes to char the skin. Let rest 8 minutes before carving.
- To serve, place vegetables on a plate, and top with hen and gremolata. Garnish with fennel fronds and rosemary buds, and drizzle with olive oil
In a small bowl, mix all ingredients. This can be done up to a day ahead and placed in the refrigerator, but is is best served fresh.