Heat large skillet or wok over medium-high heat. When skillet is hot, add avocado oil.
When oil is hot and shimmering, add diced onion and frozen vegetables. Sauté approximately 3 minutes or until onions are almost translucent, then push vegetables to edges of skillet, creating open area in center of skillet.
Crack eggs directly into center of skillet. Scramble eggs with spatula until eggs are cooked through.
Add cooked, cooled rice and butter to skillet. Cook 5 minutes, stirring frequently to incorporate ingredients, until butter has melted. Add soy sauce and stir well, cooking 1 additional minute.
Transfer fried rice to bowl. Pack rice tightly into bowl and cover with lid or plate to keep rice hot. Wipe out skillet to use again.
For the Hibachi Shrimp (Made Simultaneously with Vegetables)
Add sesame oil and avocado oil to skillet used for fried rice. Heat oils over medium-high heat until hot and shimmering.
When oil is ready, add shrimp, soy sauce, butter, lemon juice, salt, and pepper to skillet. Stir gently to incorporate, then cook until shrimp are opaque and slightly curled, approximately 5 minutes.
For the Hibachi Vegetables (Made Simultaneously with Shrimp)
Heat second large skillet or wok over medium-high heat. When skillet is hot, add sesame oil and avocado oil.
Heat oils until hot and shimmering, then add zucchini, onion, mushrooms, butter, soy sauce, salt, and pepper to skillet. Stir to incorporate, then sauté 6 to 8 minutes or until vegetables are tender.
For the Mustard Sauce
Add sesame seeds, ground mustard, honey, soy sauce, half and half, hot water, and minced garlic to blender. Blend until ingredients are fully combined to create smooth sauce, then transfer to ramekins or small bowls.
To Serve
Divide fried rice, hibachi shrimp and vegetables, and mustard sauce equally into 4 to 6 servings. Garnish with sesame seeds if desired and serve immediately.
Recipe Notes
Rice: For the best fried rice, use leftover or pre-cooked rice, rather than cooking your rice immediately before starting this recipe.
Sesame Seeds: Lightly toasting the sesame seeds will enhance their flavor, but it's totally optional.
Mustard Sauce: The mustard sauce can be prepared up to 3 days in advance and refrigerated in an airtight container until ready to serve.