Heat the oil, ghee, or butter in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the minced ginger, garlic, chopped green chili, and asafetida; sauté, stirring constantly, until fragrant, about 2 minutes.
Stir in the chopped onion, ground coriander, garam masala, turmeric, and Kashmiri red chili powder; continue to sauté, stirring occasionally, until the onion is very fragrant and softened, about 8–10 minutes. Reduce heat if the onion begins to brown.
Pour in the cream or coconut milk and stir to combine.
Add the chopped spinach in three batches, stirring well after each addition so the greens wilt before adding more; once all spinach is added, add the chopped collard greens and cover for a few minutes to help them soften.
When the greens are wilted and tender, transfer the mixture to a blender, food processor, or use an immersion blender, and blend to your desired consistency.
Return the blended saag to the pot, add the cubed paneer, and heat gently for a few minutes until the paneer is warmed through and the flavors meld; adjust salt to taste.
Serve hot with steamed rice or naan.