Place the black-eyed beans into a pan. Cover with fresh water, bring to the boil and simmer for 30 minutes or until tender. Drain.
Blanch the beans in boiling water for 1 minute. Drain, refresh under cold water and drain again.
Meanwhile, heat the oil in a frying pan, add the onion, garlic, carrot, leek and boudin and sauté until softened.
Place the beans in the pan with the oil and boudin mixture, plus the thyme, seasoning, wine vinegar, chicken stock and half of the butter. Bring to the boil, uncovered, for about 10 minutes until the liquid is reduced by a third. Set aside.
Season the fish, brush lightly with oil, then place in the pan. Simmer gently until the fish are opaque in the centre and flakes when bent. Remove from the pan and keep warm.
Remove the beans mixture from the broth using a slotted spoon and place it on warmed serving plates.
Spoon the sauce over the beans and place the cooked brill fillets on top.
Serving Suggestions: Serve the fish and beans on a warm plate with the sauce poured over, top with parsley, basil oil and a grind of black pepper.