For the rice, cook in a rice cooker as directed on package.
For the sauce, stir together the soy sauce, honey, and lime juice in a small bowl and set aside.
Heat canola oil in a large skillet over medium-high heat. Add the onion and cook, stirring occasionally, until the onion starts to soften, about 2 minutes.
Add the garlic and season with a little salt and pepper, then cook about 30 seconds.
Add the broccoli, carrot, mushrooms, bell pepper, and 2 tablespoons of the stock. Season with a little salt and pepper, and cook, stirring often, until vegetables are soft on the outside but still crunchy in the middle about 5 minutes.
Add the sauce to the pan and cook, stirring often, until the vegetables are cooked al dente.