Cook the broccolini in a large pot of boiling and slightly salted water until bright green and crisp-tender, about 6-8 minutes. Drain and transfer to paper towels. Cool tip - if you add a pinch of bicarbonate soda to the water you boil the greens in, it will make their colour much more vibrant! Just be sure not to add too much so that you can taste it.
Meanwhile, mix the tahini, soy sauce, mirin, vinegar, sesame oil, vegetable oil, and honey in a small bowl to make the sesame dressing. Season with salt to taste - you may not need a lot, as the soy is salty. You can add a dash of lemon juice to make it a little tangier as well if you wish.