In a Dutch oven or large, heavy saucepan, combine all of the dried beef ingredients except the lime juice. Bring the meat mixture to a boil, skim off any foam, reduce the heat to a low simmer, and cover. Cook for about 2 to 2¼ hours, until the meat is very tender. Cool the meat in its cooking liquid for 30 minutes. Strain the cooking liquid, reserving 1 cup. (The remaining liquid can be used as a soup stock or to enrich vegetable dishes.)

Preheat the oven to 275°F.

Tear the meat into thin shreds and transfer it back to the Dutch oven or saucepan. Add the reserved cooking liquid and simmer over medium heat until the liquid is absorbed. Pour the lime juice over the meat and toss together.

Transfer the meat to 1 or 2 baking sheets, spreading it thin. In a small bowl, combine the dried seasonings and sprinkle about half of the mixture over the meat. Bake the meat for 20 minutes, stir it well, and sprinkle with as much of the remaining dried seasonings as you wish. Bake an additional 30 to 40 minutes, until browned and dry. (The meat can be prepared ahead to this point and refrigerated for 1 or 2 days. This method does not preserve the meat, so do not leave it at room temperature.)

Transfer the meat to a blender, a handful at a time, and Purée briefly, in little bursts, until the meat is reduced to fine threads. Don’t overdo it or the meat can end up resembling sawdust.

In a heavy skillet, warm the oil over medium heat. Add the onion and sauté until softened. Stir in the chiles, tomatoes, garlic, and oregano and cook for another couple of minutes, covered. Add the browned meat and heat through, cooking uncovered until all the liquid is evaporated. Add salt to taste if you wish.

Serve the carne seca with lime wedges.