Soak the urad dal and white rice in water for at least 4 hours, then grind into a smooth, thick batter using a high-speed blender.
Transfer the batter to a bowl and allow it to ferment in a warm place for 8 to 12 hours until it has doubled in volume and smells slightly tangy.
Grease idli molds with a tiny drop of oil and steam the fermented batter for 10 minutes until the cakes are firm yet springy to the touch.
Pressure cook the toor dal with water until completely soft, then whisk or mash it into a smooth consistency.
Heat avocado oil in a saucepan over medium heat, add mustard seeds until they begin to pop, then sauté the red onion and carrots until tender.
Stir in the sambar powder, tamarind paste, and mashed dal, allowing the mixture to simmer for 10 minutes to develop a deep, zesty flavor.
In a separate small bowl, whisk the Greek yogurt with sea salt and black pepper to create a thick, savory side for extra protein.
Plate the warm idlis with a generous serving of sambar, garnish with fresh cilantro, and serve alongside the seasoned yogurt.