Bring 4 1/2 cups water to a boil in a saucepan. Preheat oven to 300 degrees. Spread ancho, guajillo, mulato, and chipotle chiles and garlic on a baking sheet. Roast until softened, about 7 minutes. Let cool slightly.
Tear chiles into pieces, discarding stems and seeds. Add to boiling water, remove from heat, and top with a smaller plate to keep chiles submerged. Let stand 30 minutes. Drain, reserving 1 cup water. Puree chiles, reserved chile water, the tomatoes and their juices, and 5 cups warm water in a blender.
Peel garlic. Pound garlic, cumin, oregano, 2 teaspoons salt, and the vinegar into a paste with a mortar and pestle.
Heat 1 1/2 tablespoons oil in a Dutch oven or other large heavy pot over medium-high heat. Season beef generously with salt and pepper. Working in batches and adding more oil as needed, cook beef until browned all over, 2 to 3 minutes. Transfer to a plate.
Reduce heat to medium. Add onion to pot, and cook until translucent, about 5 minutes. Stir in garlic paste, and cook until fragrant, about 2 minutes. Stir in beef and chile puree, and season with salt and pepper. Raise heat, partially cover pot, and simmer chili until thickened, about 2 1/2 hours. Stir in beans, and cook until heated through. Serve with sour cream, cheese, and jalapeno.