Place chicken fillets in a saucepan and cover with salted water. Once the water has come to a boil, cover with a lid and turn to simmer for 15 minutes.
Whilst chicken breasts are poaching, prepare the pistachio pesto. Chop pistachios into small chunks. Chop basil into small pieces. Place all ingredients in a bowl and combine well. Set aside.
For the miso sauce: Heat a saucepan with vegetable oil, gently fry garlic and ginger for 1 minute. Add the rest of the ingredients and using a fork whisk continuously until it forms a smooth sauce. Remove from heat.
When chicken is ready remove from water and using 2 forks shred into small pieces. Place chicken into miso sauce and over a gentle heat combine the sauce well with the chicken. If using black sesame seeds sprinkle them through the chicken once it is off the heat.
Squeeze lemon over shredded lettuce and cucumber slices. Sprinkle with salt.
Switch oven to grill setting and toast the inside of the brioche buns until nicely browned.
Butter each side of the bun generously. Layer first with lettuce, then pulled chicken, cucumber and top with pistachio pesto.