First Cook the Lentils and Roast the Carrots!:

Preheat the oven to 350 degrees F and line a baking sheet with aluminum foil.
Wash the lentils in a sieve under running water and inspect the lentils for any debris.
Add the lentils in a pan with the water or stock and bring to a boil. Then turn down the heat and simmer. Stir them now and again to prevent sticking to the pan. Simmer for about 10-15 minutes. Check for tenderness by tasting and adjust the cooking time accordingly if the lentils are still tough. Reserve to the side until needed.
Once the oven is preheated, pile the peeled and sliced carrots onto the prepared baking sheet and toss with 1/2 of the oil and a pinch of salt.
Once the carrots are evenly coated in oil, spread them out into an even layer on the baking sheet, and bake on the middle rack in the oven for about 15-20 minutes, until lightly browned and fork tender.

Then Assemble and Simmer the Soup!:
While the carrots are baking, heat the other 1/2 of the oil over medium heat in a large pot. Add finely chopped onions and sauté for 3-5 minutes.
Add minced garlic and ginger and sauté for 5 minutes longer, stirring frequently. Add curry powder and black pepper and sauté for 1 minute longer.
Pour in the vegetable stock, roasted carrots and cooked red lentils. Simmer over medium-low heat for 10-15 minutes.
Using an immersion blender puree the soup. If using a blender or food processor, puree the soup in batches.
One the soup is blended in the pot, add coconut milk. Stir until the soup is mixed thoroughly. Heat for 5 – 10 minutes, tasting occasionally and adding salt and pepper as needed.
Garnish, if you like, with a dollop of yogurt and and a sprig of fresh parsley.