Wash both types of lentils together in several changes of water. Place the lentils and 1 litre of water in a large saucepan. Bring to a boil, skimming off any residue that forms. Add the turmeric, garlic, ginger and a little salt. Simmer, covered, for 40 minutes, giving the pot an occasional stir. After the lentils have been cooking for about 30 minutes, heat the oil and butter for the tarka. Add the whole dried chillies and cumin seeds and, once they have browned, add the onion; sauté until well-browned. Add the tomatoes, garam masala and a little more salt and sauté until the masala releases oil, around 10 minutes. Pour some of the lentils into this pan, swirl and scrape the base to extract all the flavours, then pour everything back into the lentils. Cook for another 10 minutes, mashing some of the lentils on the side of the pan to make a homogenous dhal. Add a little water if the lentils are too thick (remember it will thicken further as it cools). Taste, adjust the seasoning and serve scattered with the chopped coriander.