Caramelize Onions: Heat olive oil in a pot over medium heat. Add sliced onions and caramelize for about 15 minutes, stirring regularly.
Add Spices: Reduce heat and add tomato puree, chili pepper, cumin, coriander, and minced garlic. Cook for about 1 minute.
Add Liquid: Add 1 liter of water (or vegetable/chicken broth) and mix to dissolve the tomato paste.
Add Lentils: Add rinsed lentils to the pot, increase heat to bring to a light boil, then cover and cook for 15 minutes.
Prepare Rice: Rinse rice under water 3-4 times to remove starch. After 15 minutes, add rice to the pot.
Season and Cook: Season with salt, ensuring rice is covered by liquid. Cover and simmer for 15-20 minutes until liquid is absorbed.
Let Sit: Turn off heat and let sit covered for 10 minutes.
Fry Vegetables: Slice carrots (and optional zucchini or eggplant) and fry in oil at 180°C until lightly golden. Season with salt.
Prepare Yogurt Sauce: Mix natural yogurt with minced garlic and lemon juice for serving.
Serve: Serve Mujadara topped with fried onions and vegetables, alongside the yogurt sauce.