This should serve around four people.

What You Will Need
2 corn tortillas (preferably 1 of yellow cornmeal and 1 of blue)
5 green chiles, roasted, skinned, seeded
2 cups chopped white onion
2 garlic cloves minced
1/2 teaspoon dried oregano, crumbled
some frsh oregano chopped
2 bay leaves
3 1/2 cups of vegetable stock
1 pound (or 2 medium) baking potatoes, peeled and chunked
1 teaspoon toasted cumin seeds
sea salt and fresh black pepper
1/3 cup heavy cream
2 cups of grated Monterey Jack cheese or queso blanco
see Make Your Own Mexican Cheese (Queso Blanco)
some corn oil

What Now?
Cut the tortillas into 1/4 inch wide strips and heat in a dry cast-iron skillet until dry and hot. (Or leave them uncovered at room temperature until they are dry and cripsy.)

Sauté the onions, garlic, oregano, and bay leaves in the corn oil, simmer covered, stirring once or twice, for 10 minutes. Stir in vegetable stock, potatoes, salt, cumin seeds & black pepper and bring to a boil. Remove the bay leaves (best to put them in cheesecloth like a bouqet garni). Lower the heat and simmer, partially covered, stirring once or twice, until the potatoes are tender, about 25 minutes. (At this point you can purée the soup with an immersion blender.)

Chop up the chilies. Stir in the chilies and cream and adjust the seasoning if necessary. (The soup can be prepared up to 3 days ahead. Cool it completely and refrigerate, covered. Rewarm it over low heat, stirring often, until steaming.)

To serve, the soup into wide bowls, sprinkle the cheese over the soup, and scatter the tortilla strips over the cheese. Garnish with fresh oregano.