In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the pork cubes and season with salt and pepper. Brown the pork on all sides, about 5-7 minutes. Remove the pork and set aside.
In the same pot, add the diced onion and cook until softened, about 3-4 minutes. Stir in the minced garlic and chopped jalapeños, cooking for an additional 1-2 minutes until fragrant.
Add the quartered tomatillos to the pot and cook for another 5 minutes, stirring occasionally.
Return the browned pork to the pot. Pour in the chicken broth, and add the ground cumin and dried oregano. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for about 1.5 to 2 hours, or until the pork is tender and easily shredded with a fork.
Taste and adjust seasoning with more salt and pepper if needed.
Serve hot, garnished with chopped cilantro and lime wedges on the side.