Place the broccoli florets in a steamer tray in a large pot of boiling water.
Once the water is boiling, place a lid on the pot and steam for 2-3 minutes or until broccoli is just tender.
Remove from the pot of water and steamer immediately. Set aside.
While the broccoli is steaming, heat the vegetable oil in a large cast-iron skillet over medium heat. Add the onion, carrot, and bell pepper to the skillet. Cook, stirring often, for 4 minutes.
Add the zucchini, sugar snap peas, and broccoli to the skillet.
Add the minced garlic, soy sauce, and sesame oil, then cook for 1 minute, stirring constantly.
Remove from the heat and season with sea salt and freshly cracked pepper, to taste.