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1
Light a grill.
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2
When the fire is medium hot, brush the grate with oil.
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3
Skewer the garlic cloves on a 4-inch bamboo skewer.
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4
Grill the chiles and garlic, turning occasionally, until blackened all over, about 6 minutes for the garlic and 15 to 20 minutes for the chiles.
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5
Transfer the chiles and garlic to a medium bowl, cover with plastic wrap and let cool.
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6
Peel, core and seed the chiles and cut them into 1/4-inch strips.
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7
Peel the garlic cloves.
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8
Transfer the garlic and two-thirds of the chiles to a blender.
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9
Add the cilantro, lime juice, cumin, oregano and water and puree until smooth.
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10
Season the sauce with salt and pepper and transfer to a small saucepan.
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11
Simmer over moderate heat, stirring occasionally, until the sauce is slightly thickened, about 5 minutes.
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12
In a small bowl, combine the remaining roasted chiles with the cheese.
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13
Shape the meat into 4 patties about 3/4 inch thick and season very generously with salt and pepper.
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14
Grill the burgers over a medium-hot fire for about 10 minutes, turning once, for medium-rare meat.
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15
Move the burgers away from the heat.
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16
Brush the cut sides of the buns with oil and grill until lightly toasted, about 1 minute.&
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17
Set the grilled burgers on the bottom halves of the buns.
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18
Top the burgers with the chile-cheese mixture and a generous spoonful of the salsa verde.
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19
Cover the green-chile burgers with the buns and serve right away, passing the remaining salsa verde on the side.