Heat olive oil in a large skillet on medium heat until hot but not smoking. Add oyster mushrooms and garlic, and sauté for 2-3 minutes, regularly stirring with spatula.
Sprinkle the mushrooms with a little salt, cover and cook the mushrooms for 5-7 minutes, occasionally stirring. Mushrooms should be cooked for a total of 7-10 minutes. Cover the skillet and set aside.
In the meantime, bring a large pot of water to boil, add pasta. Cook pasta according to package instructions
As you cook pasta in boiling water, blanch the broccoli by dipping the broccolini into pasta boiling water for 30 seconds, then draining it. The broccolini will turn bright green! Cut the broccoli head into flowerets and small bite-size pieces. Add broccoli pieces to the skillet with mushrooms.
Reserve 1/4 cup pasta water; drain pasta and rinse with cold water. Set aside
Add 2 tablespoons tamari sauce, 1 tablespoon honey, 1 teaspoon sesame oil, and 1/4 cup reserved pasta water to the skillet with mushrooms and broccoli, on medium heat. Stir to combine, to make sure the sauce coats the vegetables.
On medium heat, add cooked and drained pasta to the skillet, mix well until the sauce coats the pasta, taste and season with salt, if desired.
To serve, top each pasta serving with some whole cashew nuts and some finely crushed ones (use knife to crush them into smaller pieces).