Preheat the oven to 425 degrees F. Prick the potatoes with a fork and microwave until tender, 15 to 20 minutes. Transfer to the oven rack and bake until soft, about 15 minutes.
Meanwhile, finely chop the red onion. Put 2 tablespoons chopped onion in a small bowl; cover with cold water and let soak 10 minutes. Drain, pat dry and set aside for topping. Chop the poblano and grate the carrot.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the remaining red onion, the poblano and carrot; season with salt and pepper. Cook, stirring occasionally, until tender, about 5 minutes. Stir in the lentils, chili powder and cumin; cook until the spices are toasted, about 1 minute. Add the tomato paste and cook, stirring, until the vegetables are coated. Stir in the tomatoes and their juices, 1 1/2 cups water and a large pinch of salt. Simmer, stirring occasionally, until thickened slightly, about 10 minutes.
Split the potatoes open. Drizzle with the remaining 1 tablespoon olive oil and season with salt and pepper. Fluff the flesh with a fork. Sprinkle with half the cheese, then top with the chili. Sprinkle with the remaining cheese and the reserved red onion.