Melt the butter in a wide heavy pot over medium heat. Cook the onion, carrot, and celery 8 minutes until softened. Add the mushrooms and cook until they release their liquid and it evaporates, about 6 minutes.

Add the garlic and ginger and cook 1 minute.

Add the garam masala, cumin, coriander, turmeric, cayenne, and tomato paste all at once. Stir constantly for 60 to 90 seconds until the paste darkens and the spices smell toasted. This blooming step is what gives the filling depth.

Stir in the rinsed lentils and the vegetable stock. Bring to a boil, then simmer uncovered 25 to 35 minutes, stirring occasionally, until the lentils are tender and the mixture is thick enough that a spoon leaves a track.

Stir in the peas and the salt. Taste and adjust the seasoning now, before the topping goes on.

Cover the sweet potato chunks with cold salted water and boil 15 to 18 minutes, until a knife goes through with no resistance.

Drain them thoroughly and return them to the empty hot pot for a minute so the surface moisture steams off.

Mash with the butter first, then add the warm coconut milk a splash at a time along with the garam masala, salt, and pepper. Stop when it is smooth and thick enough to hold a ridge. Do not use a food processor.

Heat the oven to 400F. Spread the filling in a 9x13 inch baking dish or a similar 3 quart dish.

Spoon the mash over the filling in dollops, join them together, and drag a fork across the surface to raise deep ridges.

Bake 25 minutes until the filling bubbles at the edges, then broil 2 to 4 minutes until the ridge tips take on color. Watch it closely.

Rest 10 minutes before serving so the filling sets.