Place chiles in a large skillet over medium-low heat and gently toast until fragrant, 2 to 3 minutes per side. Be careful not to let them burn. Place toasted chiles in a bowl, cover with hot water, and soak until soft, 30-40 minutes, turning occasionally.
Drain water. Split chiles open and discard the stems and seeds. Place chiles in the bowl of a blender or food processor; add cumin, black pepper, salt, and 1/4 cup water. Purée, adding more water as needed, until mixture resembles a smooth paste. Set aside.
Return skillet to medium-high heat and melt 2 tablespoons of lard. When it begins to smoke, swirl skillet to coat and add half of the beef. Lightly brown, 2-3 minutes per side, being careful not to let burn. Transfer to a bowl and repeat with 2 more tablespoons of lard and the remaining beef. Reserve.
Let skillet cool slightly, then place over medium-low heat. Melt the remaining 1 tablespoon of lard in the skillet; add onion and garlic and cook gently for 3-4 minutes, stirring occasionally. Add the beef stock, remaining 2 cups water, and gradually whisk in the masa harina to avoid lumps. Stir in the reserved chile paste. Add reserved beef and bring to a simmer over high heat.
Reduce heat to maintain a slight simmer and cook, stirring occasionally, until meat is tender but still somewhat firm and about 1 ½ to 2 cups of thickened liquid sauce remains, about 2 hours.
Stir in brown sugar and vinegar thoroughly and add more salt to taste; gently simmer 10 minutes more. Turn off heat and let chili sit for about 30 minutes, allowing the meat to absorb some of the remaining liquid, leaving a thick, slightly fluid sauce. If chili seems too dry, stir in additional broth or water; if it seems too liquidy, allow to simmer a bit longer. Adjust flavor as necessary by adding more salt, sugar, and/or vinegar.
Reheat gently and serve in individual bowls with a dollop of sour cream on top and a lime wedge and slice of Martin’s Butter Bread on the side.
Recipe adapted from: www.epicurious.com