Rinse the rice and dal together in a fine-mesh sieve under running water until the water runs clear, then drain and set aside.

Heat the oil in a Dutch oven or deep pot over medium-high heat until the oil is shimmering and glossy. Add the cumin seeds and asafetida and cook until they just start to brown and smell toasted, about 1 minute.

Stir in the bay leaves, cinnamon stick, cloves, and dried red chili, then remove the pot from the heat. Stir in the curry leaves, green chili, ginger, turmeric, and black pepper until well combined and highly fragrant.

Add the cabbage, potato, carrot, peas, corn, and a pinch of salt to the pot. Return the pot to medium heat and cook, stirring frequently, until the cabbage begins to soften, about 5 minutes; add a splash of water if the spices start to stick to the bottom.

Stir in the rinsed rice and dal, water, nutritional yeast, and salt. Bring the mixture to a boil, then reduce the heat to medium-low to maintain a gentle simmer. Cover the pot and cook until the grains are fully tender and the vegetables are soft, about 20 minutes.

Remove the lid and increase the heat to medium-high. Stir gently and frequently for 3 to 5 minutes until the khichadi thickens into a porridge-like consistency, then remove from the heat and adjust salt to taste.

Serve warm, topped with fresh cilantro and a squeeze of lime juice.