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In a large bowl, mix the ground beef with the salt and pepper and set aside.
Next, brush the green chiles with oil and place them on the hottest part of the grill. Cook the chiles until they are charred on all sides about 5 minutes. Then remove them from the grill and put them in a bowl of ice water to cool. Remove the chiles from the ice water and carefully peel off the charred skin. Cut the stem off, remove the seeds and set aside. Take the onions and place them on the grill. Cook the onions until charred on all sides about 10 minutes and set aside.
In a blender, add half the peeled chiles and half of the charred onions. Then add in the garlic, epazote, and oregano. Blend until the ingredients come together. Add the grapeseed oil and water and continue blending until the mixture is smooth about 30 seconds. Remove mixture to a large bowl.
Roughly chop the remaining chiles and onions and mix them into the chile puree. Season, to taste.
Form the ground beef into 4 (8-ounce) patties. Brush the grill with oil and cook the patties to desired doneness, 5 minutes for medium rare, 15 minutes for well done. Put the hamburger buns on the grill until lightly toasted. Just before removing the burgers, top them with the cheese and chile mixture. Remove the patties from the grill once the cheese begins to melt and place them on the hamburger buns. Garnish with your favorite toppings and enjoy!