1. To roast the poblanos, place the chilies on a rack over a hot gas flame, on a grill or under a broiler. Cook on all sides for 3 to 5 minutes, making sure the skin is blackened. Be careful not to overcook. As soon as the skin turns black, turn the chili to blacken another portion. Place in a paper or plastic bag. Allow the chilies to sweat until they are cool enough to handle. Pull off the skin, or scrape it off with a blunt knife. Cut chilies into small pieces.
2. Next, peel the potatoes and remove the eyes or dark spots. Cut potatoes into uniform 1-inch pieces so they will cook evenly.
3. Bring a large saucepan of water to a boil over high heat. Add salt and potatoes and cook until tender, about 10 to 15 minutes. Immediately drain potatoes in colander. Fill a food mill or potato ricer with potato pieces. (Both separate the starch. Whipping or mashing releases the starch, resulting in sticky, gluey potatoes.) Pass all the potatoes through the mill or ricer in small batches. Mix in milk, butter, chilies and cheese and stir until ingredients are well incorporated. Season with salt and pepper and serve immediately.
4. Or, make up to 2 hours in advance and allow them to stand uncovered at room temperature. Reheat over medium-low heat, stirring and thinning with a little more milk, if needed.
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