Cook sweet potato cubes for 20 minutes. In the meantime, in a large pot, saute onions until they start to brown, then add garlic, carrot and leek. Saute until they start to soften. Mix in garlic paste, saute until acidity goes away. Mix in curry powder and pepper, fry for a bit.
Drain the sweet potato and mash well. Add it to the pot along with broth, lentils, coconut milk and salt. Bring to a gentle boil and cook for 30 minutes.