Mix soy sauce and 1 tablespoon chili paste in a small bowl. Spread mixture over steak and let marinate in the refrigerator for 1 hour.
Microwave the broccoli, peas, and carrots in a covered microwave-safe dish with 2 tablespoons of water for 2 minutes or until crisp tender. Rinse under cold water and drain. Mix the vegetables with the cucumbers, sesame oil, remaining chili paste, and sesame seeds. Cover and set aside.
Heat a nonstick skillet over medium-high heat. Add canola oil and heat. Then add beef and cook for 2 to 3 minutes, stirring constantly.
To serve, divide the rice evenly among 6 bowls. Evenly divide vegetable mixture over rice, followed by beef, then spinach and mushrooms. Serve.
