In a clean, dry skillet dry-roast the walnuts until lightly browned and fragrant. Remove to cool. Lightly toast the coriander seeds in the same skillet. Cool.
In a saute pan heat 2 tablespoons of the olive oil and lightly brown the chicken on both sides. Stir in the white wine and bring to the boil, scraping the pan to loosen and incorporate the brown bits (fond). Add the chicken stock, bay leaves, salt and pepper. Cook the chicken slowly on top of the stove until meat is tender; about 30 minutes.
In a food processor or blender, blend the garlic, walnuts, coriander seeds and cayenne. In the same fashion as preparing mayonnaise, slowly add the remaining olive oil and half the lemon juice. Mix well and season to taste. Transfer mixture to bowl.
Remove the chicken pieces from the saute pan using a slotted spoon. Keep chicken warm in low oven. Pour the pan juices through a strainer and then stir the juice into the walnut sauce.
In a separate bowl, beat the eggs until light and frothy. Next stir in the lemon juice. Pour the lemon/egg mixture into a saucepan and slowly stir in the walnut sauce. Heat the mixture gently, but DO NOT allow the sauce to boil. (If it boils the eggs will curdle.).
Arrange the warm chicken pieces on a serving platter and pour the sauce on top.