Place potatoes in a medium bowl; cover with cold water to prevent browning. Place chiles in a small heatproof bowl and pour the boiling water over them. Set aside until they are reconstituted, about 15 minutes. Reserving the chile-soaking water, coarsely chop the chiles (do not seed).

Pile cilantro, garlic, salt and the chopped chiles in a mortar. Pound the ingredients to a pulpy mass with the pestle, using a spatula to contain the mixture in the center for a concentrated pounding. (Alternatively, mince the ingredients in a food processor.)

Heat oil in a large skillet over medium-high heat. Add the spice paste and cook, stirring, until the garlic is honey-brown and the chiles are pungent, 1 to 2 minutes. (Make sure to use adequate ventilation.) Drain the potatoes and add along with turmeric; cook, stirring to coat the potatoes with the yellow spice, about 30 seconds. Pour in the reserved chile-soaking water and scrape the pan to loosen any browned bits; bring to a boil. Reduce heat to a gentle simmer, cover and cook, stirring occasionally, until the potatoes are fork-tender, 15 to 20 minutes.

Whisk buttermilk and cream in a small bowl.

When the potatoes are tender, pile the spinach leaves over them, cover and cook until the spinach is wilted, 3 to 4 minutes. Remove from the heat and stir in the buttermilk mixture.