Bring to a boil, then simmer on a gentle boil on medium heat for 30 minutes.
... strain the sauce, using a chinois or a fine sieve.
Bring the strained sauce to a boil and thicken with cornflour or beurre manié. Pour some cornflour into a small amount of cold fish stock, then pour it into the boiling sauce à l'américaine while whisking. Pour the cornflour liaison (or beurre manié) gradually into the sauce...
... until you obtain the desired consistency, or whisk the beurre manié into the boiling sauce. Sift the bound sauce with a chinois with metal mesh. Add the butter and whisk to make the sauce smoother. Keep warm in a bain-marie.
Peel the monkfish tail.
Fillet the tail, and cut into chunks.
Slice the asparagus into 3-4cm segments. Discard the hard, lower part.
Seed and wash the peppers.
Cut them into large trips, then make diamond shapes.
Slice the flat beans at a slant.
Cut the radishes into thin slices.
Cut the courgettes into 5cm long strips.
Reserve the vegetables.
In a wok, heat 5cl of olive oil. The bottom and sides of the wok should be coated with oil.
Sweat the onion, thinly sliced.
Add the asparagus...
... the flat beans...
... and the peppers.
Season with salt. Stir the ingredients and cook gently for 5 minutes, making sure they do not brown. Stir frequently.
Add 10cl of hot water and continue cooking for a few minutes.
Add the courgette strips...
... and the radishes, as these two vegetables require less time to cook. Add a little salt.
The vegetables should be tender but crunchy. Chop some fresh basil and sprinkle over the vegetables. Keep warm.
In a non-stick frying pan, heat dash of olive oil and sear the monkfish pieces. Cook each side for 2 or 3 minutes. Season with salt and ground pepper.
On a plate, serve 2 or 3 pieces of monkish per person, depending on how big the fish pieces are. Enjoy!