In a small bowl, combine olive oil, molasses, chopped garlic, thyme, wine and quails. Toss to coat. Cover and refrigerate for at least 8 hours, preferably overnight.
In a food processor, combine olives, anchovies, capers, basil and garlic. Add olive oil in a steady stream while processing. Stop if oil seems to “break” or fail to emulsify. This tapenade can also sit overnight.
Prepare grill to high heat. Remove quails from marinade and pat dry with paper towels. Season each with salt and pepper, then grill each quail, turning only one. Remove quails from heat but keep warm while resting.
Toss frisée with half of tapenade. Add salt and pepper to taste. To plate, place greens in the center and top with quail. Garnish with additional tapenade.