In a small bowl, whisk together the soy sauce, honey (or maple syrup), and toasted sesame oil. In a separate tiny cup, mix the cornstarch and water together until smooth to create a slurry. Set both the sauce mixture and the slurry aside for later use.
Heat the vegetable oil in a large wok or a wide skillet over medium-high heat. Once the oil is shimmering, add the minced garlic and grated ginger. Sauté for about 30 to 60 seconds until they become fragrant, being careful not to let them burn.
Increase the heat to high. Add the carrots and broccoli florets to the pan. Stir frequently and cook for about 3 to 4 minutes. If the pan seems too dry, you can add a tablespoon of water to help steam the broccoli slightly while it fries.
Toss in the bell peppers and snap peas. Continue to stir fry for another 3 minutes. The vegetables should be bright in color and tender-crisp, meaning they are cooked through but still have a satisfying bite to them.
Pour the soy sauce mixture over the vegetables and stir to coat. Give the cornstarch slurry a quick stir and pour it into the pan as well. Toss everything together for 1 to 2 minutes until the sauce thickens and becomes glossy. Remove from heat immediately.