Clean verdolagas: Remove any browned spots or bruised leaves along with the toughest part of the stems and the roots. Rinse under cold water and dry in a salad spinner.
Prepare the tomatillo sauce: Place the 1 pound tomatillos, 2 serrano peppers, 1 clove garlic, and 1/4 white onion in a large saucepan. Fill with water and simmer until tomatillos have softened, but aren't falling apart about 10 minutes. Reserve 1 cup of the cooking liquid then drain the rest and transfer the vegetables to a blender with the cilantro, ground cumin, and 1 teaspoon kosher salt. Blend until smooth. Taste and add more salt if needed.
Cook the potatoes: Rinse out the saucepan that you used to boil the tomatillos and add the potatoes. Fill with water and add a generous, five-finger pinch of salt. Bring to a boil, then reduce the heat to a simmer and cook, covered until a knife easily goes through a potato. Drain.
Cook the sauce: Heat olive oil in a large pan over medium heat. Cook until it reaches the consistency of applesauce, 5-10 minutes.
Add the verdolagas and potatoes: Add the purslane, the 1 cup reserved tomatillo cooking liquid, potatoes, and the garlic salt to the pan, stirring to coat in the sauce. Simmer over medium heat for 10 minutes, or until the verdolagas have turned a darker shade of green, the tender stems are cooked through but still slightly crunchy. Season with more salt if needed.
Serve: Spoon the verdolagas onto a casserole and sprinkle with cotija cheese, if desired. Serve with warm tortillas or as a topping for pork chops, or enjoy it as a side to pork shoulder or a vegetarian main dish.