Place the dried chiles in a medium bowl and cover with the boiling water. Let them soak until very soft, about 15 minutes, then drain the chiles and discard the soaking liquid.

Combine the softened chiles, onion, water, tomato paste, garlic, cumin, sugar, and salt in a blender. Process until the mixture forms a thick, completely smooth puree, about 1 minute, stopping to scrape down the sides of the blender jar as needed.

Melt a portion of the butter in a 12-inch skillet over medium heat. Stir in the chile puree and cook until it darkens slightly and smells fragrant, about 3 minutes.

Whisk the remaining water into the skillet until the sauce is smooth. Arrange the tofu in an even layer in the skillet and bring the liquid to a simmer.

Reduce the heat to low and simmer gently for 30 minutes — this allows the tofu to warm through and the flavors to fully meld.

Move the tofu to a serving platter. Stir the remaining butter and lime juice into the sauce, whisking until the butter is melted and the sauce is glossy, then season with salt and pepper to taste.

Pour the sauce over the tofu, sprinkle with cilantro, and serve hot with lime wedges on the side.