MAKE THE BEANS: In a large, heavy stockpot or soup pot, heat the oil over medium-high heat. Add the onions and black pepper and cook, stirring, until the onions are soft and lightly golden, about 4 minutes. Add the sausage and cook, stirring, until brown, about 4 minutes. Add the garlic, dried peas, bay leaf, and thyme. Cook, stirring, for 1 minute. Add the broth and bring to a boil, then reduce the heat to medium and cook, uncovered, until creamy and soft, about 1 1/2 hours. Remove the bay leaf. Keep warm.

MAKE THE QUAIL: Put the wine, olive oil, cane syrup, mustard, onion, garlic, salt, black pepper, and cayenne in a blender and process until smooth, about 30 seconds. Season the quail evenly with the Creole seasoning. Put them in a large 2-gallon plastic storage bag and pour in the marinade. Close the bag securely. Carefully toss to coat the quail evenly and refrigerate for 12 hours.

Preheat the grill to medium-high.

Remove the quail from the marinade. Grill the quail over medium-high heat until cooked through, about 8 minutes total, turning them every 2 minutes.

To serve, mound equal amounts of the beans in the center of each of 6 serving plates and top each with 2 quail.