Add the carrots, garlic, and ginger to a blender and blend until finely chopped. Add the onion and pulse/blend again until chopped but not watery. Alternatively you can hand chop the carrot, garlic, and onion and grate the ginger, but I find this easier.
In a large pot over medium heat, add the oil, onion mixture, and 1 teaspoon salt. Cook for about 5 minutes, stirring occasionally, until softened.
Add the cumin, turmeric, black pepper, and red pepper flakes (if using), and cook for 30 seconds, stirring constantly, to toast the spices.
Stir in the lentils, water, 1 cup coconut milk (about ½ of the can), and remaining 1 teaspoon salt. Bring to a boil, then reduce heat to low and simmer, covered, for 20 minutes or until the lentils have broken down, stirring halfway through. If it looks low on water when you stir halfway (lentils aren’t submerged), stir in another cup of water.
While the lentils cook, make the yogurt by stirring all of the ingredients together in a small bowl. Set aside.
Once the lentils are cooked through, stir in the spinach and cook for a couple of minutes, or until the spinach has wilted down. Remove from heat and stir in the lime juice and remaining coconut milk. Taste and add more salt or lime, if needed. Top with yogurt and toasted pumpkin seeds.