Preheat a grill or heavy-duty grill pan to medium-high heat (approx. 400F/200C).
Brush steak and zucchini slices with olive oil and season evenly with salt and black pepper.
Place steak on the grill and cook for 4 to 5 minutes per side until an internal temperature of 135F (57C) is reached for medium-rare.
While steak cooks, place zucchini on the grill and cook for 3 minutes per side until charred and tender.
Transfer steak to a cutting board and allow to rest for 8 minutes to retain juices.
In a small mixing bowl, whisk sour cream, heavy cream, minced garlic, chives, and lemon juice until smooth.
Slice the rested steak against the grain into 0.25-inch strips.
Assemble the bowls by placing 1 cup of rice in each, then topping with sliced steak and grilled zucchini.
Drizzle the prepared creamy sauce over the steak and serve immediately.