Put the chiles on a small rimmed baking sheet and toast in the oven until fragrant, about 4 minutes. Don't let them burn or they will turn bitter. Transfer the chiles to a medium heatproof bowl and cover with boiling water. Cover with plastic wrap and let the chiles soak until softened, 45 minutes to 1 hour.
Drain the chiles then remove and discard the stems. Split open each chile and scrape out the seeds with the back of your knife. Discard the seeds and transfer the chiles to a blender. Add the cumin, half of the diced onion, half of the garlic, 1/2 cup of the beef stock, 1 teaspoon salt and 1 teaspoon black pepper. Blend, occasionally scraping down the sides of the blender, until a smooth, slightly fluid paste forms (you want to eliminate all but the tiniest bits of skin).
Heat a medium skillet over medium-high heat. Add the olive oil. When the oil is hot, add the chile paste and cook until slightly darkened, 4 to 5 minutes. Remove from the heat and set aside.
Heat a large, heavy-bottomed pot over medium-high heat and melt 2 tablespoons of the lard (or heat 2 tablespoons of the vegetable oil). Season the beef cubes with salt and pepper. When the lard begins to smoke, swirl the pot to coat and add half of the beef. Cook, lowering the heat if the meat threatens to burn, until lightly browned, about 3 minutes per side. Transfer to a bowl and repeat with 2 more tablespoons of the lard and the remaining beef. Set aside.
Melt the remaining 1 tablespoon lard (or heat the remaining 1 tablespoon vegetable oil) in the pot. Add the remaining diced onion and garlic and cook gently over low heat, stirring occasionally, until softened, 3 to 4 minutes. Add the beef back to the pot along with any juices. Then add 2 cups water and the remaining 2 cups beef stock. Stir in the reserved chile paste and bring to a simmer over high heat, scraping the bottom of the pot with a wooden spoon to loosen any browned bits. Lower the heat to maintain the barest possible simmer (just a few bubbles breaking the surface) and cook, uncovered, stirring occasionally, until the meat is tender, about 2 hours.
Thoroughly stir the masa harina, brown sugar and vinegar into the chili. Gently simmer for a few minutes until the sauce has thickened. Taste and adjust seasonings as needed.
Serve in individual bowls with a dollop of crema, shredded cheese, white onion and a lime wedge.
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