Rinse and soak the rice - Rinse the rice in cold water until the water runs clear. Then, soak the rice in cold water for at least 30 minutes.
Boil the rice - Drain the soaked rice and add it to a large pot with 4 cups of water and 1 1/2 teaspoons of salt. Bring the water to a boil, then reduce the heat to low, cover the pot with a tight-fitting lid, and cook for 15 minutes.
Grill the vegetables - While the rice is cooking, heat a large skillet or grill pan over medium-high heat. Add 1/4 cup of olive oil and grill the eggplant, zucchini, and red bell pepper until they are tender and slightly charred, about 5-7 minutes per side. Remove the vegetables from the skillet and set them aside to cool.
Assemble the tahdig - Once the vegetables are cool enough to handle, arrange them in a layer over the rice in the pot, pressing down lightly. Sprinkle the crumbled feta cheese and chopped kalamata olives over the vegetables. Cover the pot with a clean kitchen towel and the lid and cook over medium heat for 10 minutes to create a crispy crust at the bottom of the pot.
Make the lemony tahini drizzle - In a mixing bowl, whisk together 1/4 cup of tahini, the juice of 1 medium lemon, 2 minced garlic cloves, 1/2 teaspoon of cumin, 1/2 teaspoon of paprika, 1/4 teaspoon of black pepper, and 1/4 cup of water until smooth and creamy.
Serve and enjoy! - To serve, use a spatula or knife to loosen the tahdig from the sides of the pot, then carefully invert the pot onto a large platter. Garnish the tahdig with chopped parsley and serve with the lemony tahini drizzle on the side.