In a shallow dish, whisk together 1 tablespoon olive oil, soy sauce, smoked paprika, and black pepper. Coat the steak thoroughly and marinate for at least 15 minutes.
Preheat an outdoor grill or indoor grill pan to medium-high heat, approximately 400°F (200°C).
Toss the zucchini rounds with the remaining 1 tablespoon of olive oil and a pinch of salt.
Place the steak on the grill and cook for 5 to 7 minutes per side, or until the internal temperature reaches 135°F (57°C) for medium-rare.
Arrange zucchini slices on the grill and cook for 3 to 4 minutes per side until tender and distinct char marks appear.
Transfer the steak to a cutting board and allow it to rest for 10 minutes to retain juices.
In a small mixing bowl, combine the sour cream, lemon juice, minced garlic, chopped parsley, and kosher salt. Whisk until smooth.
Slice the rested steak against the grain into thin strips.
Assemble the bowls by portioning 0.5 cup of cooked rice into four bowls. Top each with equal portions of sliced steak and grilled zucchini.
Drizzle the garlic-herb cream sauce over each bowl before serving.