Rinse the red lentils 2 to 3 times and drain off the extra water.
Melt the butter in a large pot on medium heat. Add the onion, garlic, carrot, and potato, and cook for 1 to 2 minutes.
Add the paprika, black pepper, turmeric, cumin, and salt. Stir, then add the chopped tomato and the rinsed lentils and mix well.
Pour in 3 to 4 cups of hot water. Cover and cook on medium heat for about 25 to 30 minutes, until the lentils break down and the potato and carrot are fork soft.
Turn off the heat and let the soup cool for a few minutes.
Blend until smooth and creamy, using a hand blender or working in batches.
Add a splash of hot water if it is too thick, and adjust to the texture you like.
Pour into bowls and top with whipping cream, chilli flakes, and fresh coriander. Serve hot.