Preheat broiler to high. On a large rimmed baking sheet, arrange tomatillos, poblanos, cubanelles, serranos, onion, and garlic cloves in an even layer. Broil until vegetables are deeply charred, flipping tomatillos and peppers halfway, 10 to 15 minutes. (Watch closely.) Remove sheet from oven and let vegetables cool.

Meanwhile, heat a large Dutch oven over medium high. In a large bowl, season pork with the oil, 2 tablespoons salt, and 1 teaspoon pepper. Add pork to Dutch oven in an even layer, and cook, undisturbed, for 5 minutes, or until one side is browned. Stir pork and flatten to an even layer, and cook undisturbed again, about 5 minutes more. Continue to cook, stirring now so pork gets browned all over, about 5 minutes more.

Add cumin, oregano, and coriander and stir so meat is evenly coated in spices. Cook for about 30 seconds, or until the spices are fragrant.

In a blender, combine roasted vegetables, broth, and 1 tablespoon salt. Blend until smooth; pour into pot. Return the pork to the pot and increase heat to high. When liquid just begins to boil, reduce heat to low.

Cook, covered, stirring occasionally, for about 1½ hours, or until the pork falls apart easily and the sauce has reduced and thickened.

Remove lid, and cook uncovered for an additional 45 minutes, stirring frequently, until sauce has thickened further. Season to taste with salt and pepper.