Season pork with salt and pepper. In a large Dutch oven, heat 3 tablespoons oil over medium-high heat. Working in batches so as not to crowd the pan, sear meat until brown, about 3 minutes per side, and set aside on a platter. Add more oil, as needed, and heat between batches.
Add 1 tablespoon oil, onions, and garlic. Cook, stirring, for 1 minute. Add stock, stirring up brown bits from bottom of pan with a wooden spoon, for 1 minute.
Return pork to pan along with Anaheim chiles. Bring to a boil. Reduce to a simmer, and cook, partially covered, for 30 minutes. Stir in tomatillos and jalapenos. Return to a simmer, and cook until pork is cooked through and tomatillos are falling apart, 30 to 45 minutes more. Taste and adjust for seasoning. Serve with cilantro leaves, tortillas, and sour cream on the side.