Preheat oven to 400°F (conventional) or 350°F (convection). Cook the rice according to package directions. Wash the zucchini and slice it. Peel and finely dice the onion and garlic.
Heat the olive oil in a pan and fry the zucchini slices until golden brown. Remove the zucchini from the pan and set aside.
Using the same pan, brown the ground beef. Add the onions and garlic, and season with oregano, basil, and thyme. Continue to cook for 3-5 minutes. Add the zucchini slices, diced tomatoes, sour cream, and rice. Mix everything together and season with salt and pepper.
Pour the zucchini, ground beef, and rice mixture into a casserole dish and top with crumbled feta cheese. Bake for about 20 minutes.