ONE DAY AHEAD: Wash the quail and pat it dry. Combine the honey, 1 cup olive oil, vinegar and fresh black pepper in a large bowl until well mixed. Toss in the quail and mix until well coated. Allow to marinate overnight in the refrigerator, or for 2 hours at room temperature.
Light the barbecue or preheat the broiler.
In a 12 to 14-inch saute pan, heat 4 tablespoons olive oil over medium high heat. Drain the potato cubes and shake them dry. Add the potatoes to the hot oil and saute until light brown, stirring constantly, about 4 to 5 minutes.
Add the olives, fennel, and garlic and continue cooking 4 to 5 minutes, until the fennel is softened but still firm. Add the Strega, flame it, and allow to boil for 2 minutes, until reduced by half. Remove from the heat and set aside.
Place the quail on the grill and cook until just medium. Remove and allow to rest 1 minute. Place the potato mixture on a large platter, place the quails over the potatoes and serve.