Mix together ingredients for hibachi chicken in a small bowl, then pour over chicken. Cook chicken with sauce in a large skillet over med-high heat for 10 minutes or so, stirring occasionally until fully cooked through. Remove from pan and wipe pan clean.
Meanwhile, cook rice in a rice cooker or on the stovetop according to package directions. Alternatively, make rice up to 2 days before. Mix ingredients for mustard sauce together at the same time.
After chicken is finished cooking, add olive oil to the pan, then add vegetables and season with salt & pepper and soy sauce, cooking for 5 minutes or so until veggies are tender-crisp. Remove from heat and set aside.
Melt butter in the same pan, then saute garlic for 30 seconds until fragrant. Add in rice and soy sauce, cooking for 5 minutes until rice is heated through. Make a hole in the center of rice and crack in egg, scrambling until egg is just set. Toss rice and stir in green onions, then remove from heat and plate rice along with chicken and vegetables.
Serve chicken, rice and vegetables with mustard sauce on the side, then serve and enjoy!