Prepare the sauce: In a small bowl, whisk together sesame oil, honey, soy sauce, and sesame seeds. Set aside.
Blanch the spinach: Bring a small pot of water to a boil. Add spinach for 30 seconds, until just wilted. Remove with a slotted spoon, transfer to a plate, and gently squeeze out excess water.
Cook the vegetables: Heat a large skillet over medium heat. Add olive oil. Once hot, add onion, carrots, and shiitake mushrooms. Cover and sauté for 5–7 minutes, until mushrooms are tender and carrots are softened.
Add zucchini noodles: Toss in the zucchini noodles and cook for 2–3 minutes, until al dente. Transfer to a colander and let excess liquid drain. Return the noodles and veggies to the skillet.
Combine & serve: Add spinach back to the skillet, pour in the sesame soy sauce, and toss well to coat. Cook for 1 more minute to warm through. Serve immediately, garnished with toasted sesame seeds.