Marinate the steak and shrimp. In a small mixing bowl, whisk together. the soy, mirin, garlic, ginger, and sesame oil. Place the shrimp and steak in two separate bowls or ziplock bags. Divide the marinade evenly between the steak and shrimp and toss well to coat. Season each with kosher salt and white pepper. Marinate for at least 1 hour, up to 8 hours.
Make the yum yum sauce. The sauce gets better as it sits! In a small bowl, whisk together the mayo, tomato paste, sriracha, garlic powder, onion powder, rice vinegar, mustard, white pepper, and honey. Season to taste with salt and store in the fridge until you're ready to serve.
Cook the shrimp. Heat a large wok or nonstick deep skillet over medium heat for 5 minutes. Add the oil and once the oil is hot, add the shrimp in a single layer in the pan. Cook for 2-3 minutes per side, until lightly browned and cooked through. Transfer to a plate.
Cook the steak. Add the steak pieces to the same skillet that you cooked the shrimp in. Cook for a total of 5-6 minutes, until the steak pieces are browned on all sides. Transfer the steak to a plate.
Saute the veggies. Melt the butter in the skillet and add the onions and mushrooms. Saute for 3-4 minutes, tossing the veggies with the butter. Add the carrots and cook for 2-3 minutes before adding the zucchini. Season everything with salt and pepper, reduce the heat slightly and cook until the veggies are tender.
Serve. Divide the steak and shrimp into bowls and serve with fried or steamed rice, the sautéed veggies, and top with the yum yum sauce and scallions. Drizzle the meat with Japanese BBQ sauce, if desired.