In a bowl or pan, cover the morita chiles with boiling water. Cover and let the chiles rehydrate for 15 minutes. Once the soaking water has cooled, open the chiles with a small paring knife and remove the seeds if you want to dial down the heat on this dish.
While the moritas are rehydrating, roast the tomatillos and onion under a broiler at 500 F for about 15 minutes, turning halfway through. The tomatillos should be squishy and have a light char.
In a large pot or dutch oven, heat 2 tablespoons of oil at medium high heat. Season the pork with salt and pepper, add it to the pot in batches so that the meat is in a single layer. Sear the meat, stirring occasionally, letting a nice brown fond form at the bottom of the pot.
Return all the meat back to the pot and add enough water just to cover. Bring to a boil then reduce heat to simmer. Using a wooden spoon,loosen up the fond from the bottom of your pot, pulling that meaty flavor into the cooking liquid. Cover and let simmer.
In a blender or food processor, add the charred tomatillo, onion and garlic along with the rehydrated morita chile as well as its cooking liquid - straining out any left behind seeds. Season with salt and pepper and blend until smooth.
Add the sauce into the pot where the pork is simmering. Continue to simmer the pork in the sauce, covered on medium low for about 30 minutes.
Add potatoes to the pot and season well with salt (start with 2 teaspoons of salt and continue to taste as the potatoes soak in seasoning) and pepper. Continue to simmer on medium low until the potatoes are tender.
Once the potatoes are cooked, add in the purslane and cover. After 5 minutes, remove from heat but keep the lid on as the purslane will continue to gently cook in the residual heat for another 5 minutes.
Taste that saucy broth, adding more salt or pepper as needed. Serve with beans and tortillas.