Soften the aromatics: Heat the olive oil in a large Dutch oven or heavy soup pot over medium heat. Add the red onion, garlic, grated ginger and half the sliced chili. Cook, stirring often, for 5 to 6 minutes until the onion is soft and translucent but not browned.
Wake up the spices: Stir in the cumin seeds and toast for 20 to 30 seconds until fragrant, then add the garam masala and stir constantly for another 30 seconds. Do not walk away — the moment the kitchen smells warm and toasty, you are ready to move on.
Pile in the carrots: Add all the grated carrots and the salt, stirring well so every strand is coated in the spiced oil. Cook for 3 to 4 minutes, stirring now and then, until the carrots just begin to soften and sweeten.
Add lentils and stock: Stir in the rinsed red lentils, then pour in the vegetable stock. Bring to a boil, then reduce to a gentle simmer. Cook uncovered for about 25 minutes, until the lentils have completely broken down and the soup looks thick and golden.
Blend it your way: For a rustic, hearty texture, blend just half the soup with an immersion blender right in the pot. For a fully silky bowl, blend it all. If it feels too thick, stir in a splash of hot water until it looks right.
Finish bright and serve: Squeeze in the juice of half the lime and taste for salt and pepper — the flavors should be warm, gingery and just a little tangy. Ladle into warm bowls and top each with a swirl of yogurt, cilantro leaves, the remaining sliced chili, a drizzle of chili oil if you like, and lime wedges on the side.