Puree the mint, dill, almonds, lemon zest and lemon juice with the water. Add the cheese and salt, mix. Stir in the oil.
Bring the stock, lemon juice, onion, garlic, bay leaf and pepper to the boil in a pan. Add the chicken, reduce the heat, cover and simmer for approx. 20 mins. Remove the chicken, pull away the meat using two forks.
Add the cabbage to the stock, simmer for approx. 5 mins., season with salt. Add the beans, simmer for approx. 5 mins. Add the chicken, heat gently. Serve the chicken and beans with the stock in deep dishes, top with the pesto and herbs, drizzle with oil.