Place the mushrooms in a bowl. Cover them with hot water and let them soak until soft, about 30 minutes. Remove the mushrooms, rinse them and cut off the tough stems. Slice the mushroom caps.
Meanwhile, bring a saucepan of salted water to a boil. Cut the asparagus on the bias in 3 or 4 pieces, discarding the tough white bases (about 1/2 inch from the end). Cut the carrots in diagonal pieces about the same length as the asparagus pieces.
Add the asparagus to the boiling salted water; it should be covered generously. Boil until the pieces are barely tender, about 2 to 3 minutes; to check, lift a few on a slotted spoon and pierce them with a knife tip. Drain the asparagus, reserving the liquid. Rinse the asparagus with cold running water and drain well.
Combine the asparagus cooking liquid, carrots, mushrooms, and a pinch of salt in the saucepan. Bring to a boil. Cover and simmer until the carrots are just tender, about 5 minutes. Drain well. (This liquid can make a tasty stock!)
For the dressing, whisk the soy sauce, 2 tsp. of hoisin sauce, and 2 tsp. of vinegar in a small bowl until combined. Whisk in 2 tsp. of vegetable oil and a little salt, pepper, and hot sauce.
Heat 2 to 3 tsp. of vegetable oil in a skillet over medium heat. Add the mushrooms, asparagus, and carrots and a pinch of salt and pepper. Cook until hot, about 30 seconds. Add the dressing and heat for a few seconds, shaking the pan. Turn off the heat, add the green onion and sesame oil and toss to combine. Taste and adjust the amounts of salt, pepper, hoisin sauce and vinegar.