Melt the butter in a large heavy pot over medium heat. Add the chopped onion and a pinch of the salt and cook 6 to 8 minutes, until soft and translucent with no color.

Stir in the garlic and grated ginger and cook 1 minute more, until fragrant.

Add the curry powder, cumin, turmeric and cayenne. Stir constantly for 60 seconds, until the spices darken a shade and smell toasty. Add another knob of butter if the pot looks dry.

Add the cubed sweet potato and stir to coat every piece in the spiced butter.

Pour in the broth, add the remaining salt and the black pepper, and bring to a boil. Reduce to a simmer, cover partly, and cook 20 to 25 minutes, until a knife slides into a cube with no resistance.

Take the pot off the heat and blend with an immersion blender for 2 to 3 minutes, until completely smooth. For a countertop blender, work in two or three batches, filling the jar no more than halfway.

Return the pot to low heat, pour in the coconut milk except for 2 reserved tablespoons, and stir until uniform and warmed through, about 2 minutes.

Off the heat, stir in the garam masala and the lime juice. Taste and add more salt and lime until the soup tastes savory rather than sweet.

Serve topped with the reserved coconut milk, chopped cilantro, toasted pepitas and cracked black pepper.