Preheat a grill to medium heat (350° to 400°). Put chiles, tomatillos, and onion in a very large bowl. Drizzle with about 3 tbsp. oil and turn to coat well. Grill vegetables, covered, turning as needed, until softened and charred in spots, about 12 minutes. Let cool.
Meanwhile, heat 3 tbsp. oil in a 6- to 8-qt. pot over medium-high heat. In three or four batches, brown pork pieces until golden brown, adding more oil as needed, 20 to 30 minutes. Transfer pork with a slotted spoon to a bowl.
Stem chiles, but don't peel or seed them.
Return pot to medium heat, add garlic, and cook until pale brown, about 2 minutes. Stir in cumin, coriander, oregano, 1 tsp. salt, and the pepper; let sizzle 1 minute. Stir in grilled vegetables and cook, uncovered and stirring occasionally, 5 to 8 minutes to blend flavors.
Add stock, cover pot, and bring to a boil; then reduce heat to maintain a simmer. Simmer 20 minutes, covered.
In batches, blend vegetables with their liquid, the cilantro, and epazote (if using) until almost smooth. Fill blender no more than half-full and cover blender top with a towel, since hot liquids can spurt up.
Pour green chile sauce back into pot, add pork, and simmer, covered, over low heat until pork is very tender, about 1 hour. Season with 2 tsp. salt, plus more to taste.
Ladle into bowls and top with goat cheese, radishes, pepitas, and chopped cilantro. Serve with tortillas.
*Find epazote, an earthy-tasting, large-leafed herb, at Mexican grocery stores (look for the fresh herb; it has almost no flavor when dried). To warm tortillas, wrap in a kitchen towel and microwave 1 minute.