Place the walnuts into a food processor and blend to fine crumbs.
Brush the Dijon mustard onto the chicken fillet slices and season with salt and freshly ground black pepper.
Place the ground walnuts into a large bowl. Add the chicken slices and roll in the walnuts to coat completely.
Heat a frying pan until hot then add the olive oil. Place the chicken into the frying pan and fry for 3-4 minutes on each side, or until golden and completely cooked through. Remove from the pan and drain onto kitchen paper.
For the salad, chop half of the celery into small chunks, and slice the remainder into 5cm/2in long strips.
Place the olive oil and thyme leaves into a bowl, then add the celery strips. Toss the celery to coat in the thyme oil and season, to taste, with salt and freshly ground black pepper.
Heat a griddle pan until smoking. Place the celery strips onto the griddle and char for 1-2 minutes, until marked by the griddle and heated through.
Place the celery chunks and remaining salad ingredients into a bowl and mix well.
For the mayonnaise, place the egg yolks, mustard and white wine vinegar into a food processor and blend.
With the processor still running, slowly pour in the sunflower oil and olive oil, drop by drop at first, then faster as the mixture thickens, alternating between the two oils as you go. Continue blending until all the oil is incorporated and a thick mayonnaise is formed. Transfer the mayonnaise to a clean bowl and season, to taste, with salt and freshly ground black pepper.
To serve, add the mayonnaise to the bowl of salad and mix well. Place the salad mixture into the centre of each of four plates, top each with pieces of the walnut chicken and pieces of griddled celery.