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Place oil and 2 tablespoons butter in a large pan over medium-high heat. Add chopped green chilies and onion. Saute for about 5 minutes, or until softened. Add clove of garlic, cook for one additional minute or until fragrant. Add corn, salt, pepper and oregano. Turn off heat, set aside.
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Place potatoes in a large pot. Pour chicken broth over the potatoes in the pan. Cover with a lid and set heat to high. After the broth comes to a boil, reduce heat to medium high and cook for five minutes. Turn heat off. Add the vegetable mixture to the cooked potatoes.
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Using the pan that previously held the cooked vegetables, melt 3 tablespoons butter. Add 1/3 cup of flour, whisking with wire whisk. Cook for about 1 minute over medium heat. Slowly add milk about 1/2 cup at a time, whisking while adding milk. Cook for about 5 minutes or until thickened.
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Add the milk mixture to the vegetable/chicken broth mixture. Continue to cook over medium heat until heated through. Add grated cheese. Keep warm until ready to serve.