Preheat grill to medium. Make sure the bars are clean and well-oiled.
Toss chicken fillets in olive oil, sea salt and pepper. Place on grill and cook for 7 minutes on each side. Remove from grill and rest.
Snap off the woody ends of the asparagus. Chargrill until al dente, about 1-2 minutes, depending on thickness of asparagus. Remove from heat.
Blanch snow peas and sugar snap peas separately in boiling salted water until al dente. Refresh in iced water.
Top and tail snow peas and sugar snap peas. Cut snow peas diagonally in half. Cut asparagus into diagonal lengths about the size of the sugar snap peas. Finely cut the fungi. Peel the daikon and cut into matchsticks. Slice chicken into 1cm strips.
For the dressing whisk together all ingredients except the oil in a mixing bowl. Add oil in a thin stream, whisking continuously until emulsified. Adjust seasoning to taste.
Place vegetables in a large bowl with spinach leaves, chicken pieces and dressing. Gently combine and share over four plates. Garnish with micro herbs and serve.