Pat the pork dry and season with 1 teaspoon salt and the pepper. Heat oil in a heavy pot over medium-high heat. Brown pork in batches, turning occasionally; transfer to a plate.
Place tomatillos, jalapeños and onion on a lined baking sheet. Broil, turning as needed, until softened and lightly charred, about 8–12 minutes. Cool briefly.
Blend the roasted vegetables with garlic, cilantro, oregano, remaining ½ teaspoon salt and ½ cup broth until mostly smooth. Vent the blender carefully if the vegetables are still hot.
Return pork and its juices to the pot. Add sauce and remaining ½ cup broth. Bring to a simmer, partially cover, and cook gently for 1 ½–2 hours, stirring occasionally, until fork-tender. Add broth if needed.
Uncover and simmer briefly if the sauce needs thickening. Adjust salt and serve with lime and warm tortillas.