Place the meat in a large pot or small Dutch oven with the unpeeled onion, unpeeled garlic, 1 teaspoon salt, and ½ teaspoon black peppercorns. Add water to cover by about 1 inch. Bring to a boil over high heat and immediately reduce heat to maintain a low, rolling boil; skim off any froth that rises to the surface. Cook, partly covered, for 45 minutes, or until the meat is tender. Lift out the meat into a bowl, letting it drain very well. Set aside. Strain the stock through a mesh sieve. You should have 3 or 4 cups. Wipe out the pan and pour the stock back into it; set aside.

Meanwhile, bring 2 cups water to a boil in a small saucepan, add the chiles and cook uncovered for about 5 minutes or until softened; drain and reserve.

Cut the unpeeled pumpkin or squash (I peeled it before cooking) into 8 equal chunks, removing any seeds and strings. Add the chunks to the stock and bring to a boil over high heat. Reduce the heat to maintain a low, rolling boil and cook for about 30 minutes, or until tender. Transfer to a colander and let cool to room temperature. (You can freeze the stock for soup.) Scrape the flesh into a bowl and discard the skin. Mash thoroughly with a potato masher or pestle. Set aside.

Place the pumpkin seeds in a small, heavy skillet over medium-low heat; toast, stirring and shaking the pan, until they begin to swell up and pop, 3-5 minutes. Set aside.

Grind the cumin, coriander, and remaining peppercorns to a powder using an electric coffee grinder or a mortar and pestle. Coarsely chop the remaining onion and garlic. Purée in a blender with the pumpkin seeds, ground spices, chopped tomatoes, and the chiles. You may need to add a little stock to the blender.

In a medium saucepan, heat 1½ tablespoons of the lard or oil over medium-high heat until rippling. Add the puréed mixture, stirring to avoid splattering. Reduce the heat, cover, and cook until the fat starts to separate, about 15 minutes. Add the reserved mashed pumpkin or squash and the vinegar, stirring to mix well, and cook, covered for 10 minutes. Taste for salt and add more if needed.

While the pumpkin mixture cooks, heat the remaining lard or oil in a skillet over medium heat and brown the meat lightly for about 5 minutes, letting it get a little crisp but not dried out.

Spoon the seasoned pumpkin onto a platter and top with the meat.