Heat the butter over a medium heat and fry the bread on both sides until golden brown then set aside.
Crush the garlic and add to a large mixing bowl with the egg yolk.
Whisk together then add a little oil and whisk constantly.
Gradually pour in the oil in a steady stream while continually whisking, ensuring that all the oil is incorporated into an emulsion before adding more oil.
Season to taste and remove the aioli from the bowl and place in a small bowl for serving, leaving two tablespoonfuls.
Peel the carrot, onion and leek and chop into 1 cm pieces.
Add the oil to the pan over a medium heat and add the vegetables to soften for 3 minutes.
Add the fish stock, wine, bouquet garni and saffron (if using), add simmer for 15 minutes.
Place the fish fillets in the stock and simmer over a low heat with the lid on for about 15 minutes or until the fish is cooked.
Carefully remove the fish and set aside in a warm place.
Add two large spoonfuls of the cooking liquid to the aioli and whisk to incorporate.
Place the sieve over the bowl and strain the remaining stock into the aioli to create a smooth mix.
Return the sauce to the pan, along with the monkfish and heat through.
Check the sauce and add whisk in more aioli if you prefer.
Serve the bread with the aioli, fish and sauce.