In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for four minutes until they become translucent and fragrant.
Stir in the garlic, sweet paprika, ground black pepper, crushed red pepper flakes, diced tomato, tomato paste, and tatli biber salcasi to the pot. Cook for a few minutes, stirring occasionally, until the tomatoes soften and release their juices.
Rinse the red lentils under cold water and add them to the pot along with the vegetable stock (or water). Stir to combine all the ingredients. Raise the heat to high to bring the pot to a boil.
Once boiling, add the rice, coarse bulgur, dried mint, and salt to the soup. Give it a good stir, then place a lid on the pot, returning the heat to medium.
Cook over medium heat for 25-28 minutes or until the lentils and rice are fully cooked and tender. (If you use whole red lentils instead of split red lentils, they will take a bit longer and may also require a little extra water). Stir occasionally to prevent sticking. Add water if the consistency of the soup becomes thicker than you would like.
While the soup is simmering, you can prepare the optional topping. In a small saucepan, heat the olive oil over medium heat. Stir in the paprika, crushed red pepper flakes, and salt. Turn off the heat and let the spices release their flavors into the oil as it cools.
When the soup is ready, taste and adjust the seasoning if needed. Serve it hot, garnished with a drizzle of the optional chili oil topping, a spoonful of plant-based yogurt, and/or fresh parsley leaves if desired.