Pour the oil in a small skillet over medium heat. Lay the stemmed and seeded chiles and garlic cloves in the oil. Turn the chiles and garlic back and forth until the chiles are toasty and the garlic cloves are light brown. Remove the chiles to a blender jar, and add the sherry vinegar and salt. Let the garlic and oil cool for about 10 minutes. Blend the chiles and vinegar and stream in the cooled oil.
In a medium 10-inch skillet set over medium heat, sauté the diced potatoes in the red chile dressing, until the potatoes are soft and easy to mash, about 20 to 25 minutes. Mash them a few times with an old fashioned potato masher and add the chopped greens. Cover and let the flavor blend and the greens wilt slightly. Taste for seasoning, adding salt if necessary. Serve with a sprinkling of the cheese, a stack of warm tortillas and your favorite red chile tomatillo salsa.