In a shallow dish or large resealable bag, combine the soy sauce, 1 tablespoon olive oil, lime juice, minced garlic, black pepper, and smoked paprika (if using). Add the steak, ensuring it's fully coated. Marinate at room temperature for 15 minutes while you prep other ingredients, or refrigerate for up to 2 hours for deeper flavor.
Prepare 2 cups of rice according to package instructions so it's ready when the steak and zucchini are done. In a small bowl, whisk together all sauce ingredients (mayonnaise, sriracha, soy sauce, honey, garlic, and water) until smooth. Set aside.
Preheat a grill, grill pan, or large skillet over medium-high heat. Brush the zucchini planks lightly with olive oil and season with salt and pepper. Grill for 3-4 minutes per side, until tender and marked with grill lines. Remove to a plate and set aside.
Remove the steak from the marinade, letting excess drip off. Grill for 4-6 minutes per side for medium-rare (135°F internal temperature), or until desired doneness is reached. Transfer to a cutting board and let rest for 5-10 minutes.
Thinly slice the rested steak against the grain. Cut the grilled zucchini planks into bite-sized pieces. Divide the cooked rice among four bowls. Top with sliced steak and zucchini pieces.
Drizzle the prepared sauce generously over each bowl. Garnish with chopped cilantro, sliced green onions, and sesame seeds if desired. Serve immediately with lime wedges on the side for squeezing over the top.