Place in boiling water and cook until soft. Cool down in cold water and drain. Roughly crush by hand. Finely chop the fresh herbs and add to the potatoes. Combine the vinegar, mustard and sugar and whisk together. Slowly add the olive oil. Add the vinaigrette to the potatoes and mix thoroughly.
Cut the peppers in half, de-seed and place on a tray. Drizzle olive oil over the peppers; add a pinch of rock salt and thyme. Place in the oven and roast until blistery; take out of the oven and cool. When cold, skin and slice thinly. Retain the olive oil the peppers were cooked in for re-heating the vegetables. Take the asparagus, chop off the root end and discard. Take the remaining stalks and halve equally then take the spears and trim the bottoms off. Add the asparagus into boiling salted water. Cook until tender. Cool under cold water and separate spears from the stalks, chop the stalks diagonally and put to the side. Next slice the shii-take mushrooms and place to the side.
Place in a blender the basil leaves, the French mustard, sugar and vinegar. Blend together and slowly add the olive oil until you obtain a good consistency. Check for seasoning and place in a bottle for pouring.
To prepare the fish, skin and trim and cut each fillet in half diagonally and season the skin side (this will be the presentation side).
Heat a large frying pan, add oil. The pan should be smoking. Place the fish presentation side down in the oil and sear for around 30 seconds. Add a few drops of oil to the pan; toss the pan so the tomatoes are coated in oil. This will soften them and allow them to take colour. Place the pan under the grill, be careful not to over cook. The Turbot should be quite spongy to touch. Next re-heat the potatoes and place in the centre of a hot plate. In a large sauté pan, add the oil the peppers have been cooked in and heat. When hot enough add the sliced mushrooms and soften. Add the peppers and sliced asparagus, season and add one large pinch of Cajun spice. Add the asparagus spears and toss until piping hot.
On the plate, arrange some vegetables over and around the potatoes. Place a fillet of Turbot on top of the vegetable, add more vegetables and place the final fillet on top.