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1
Place the pork, chorizo, and garlic in a large bowl and use your hands to evenly combine.
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2
Divide the meat into 4 equal portions.
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3
Shape each portion into an even 1/4- to 1/2-inch-thick patty (the patties will be very thin).
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4
Using your thumb, make a shallow 1-1/2-inch-wide indentation in the center of each patty (this helps the burgers cook more evenly).
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5
Transfer the patties to a plate and refrigerate while you prepare the grill.
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6
Heat a grill pan or outdoor grill to medium-high (about 375 degrees F to 425 degrees F).
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7
When the grill is ready, use tongs to rub the grate with several layers of paper towels dipped in vegetable oil.
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8
Place the chiles on the grill, close the grill, and cook, turning occasionally, until softened and charred on both sides, about 10 minutes.
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9
Remove to a medium bowl and cover tightly with plastic wrap or a lid.
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10
Let the chiles steam until the skins can be easily peeled away, about 10 minutes.
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11
Meanwhile, grill the avocado.
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12
Brush the cut sides of the avocado halves with vegetable oil and season with salt.
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13
Place them cut-side down on the grill and cook until grill marks form and the avocados soften, about 4 to 5 minutes.
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14
Remove to a cutting board or work surface until cool enough to handle, about 5 minutes.
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15
Meanwhile, peel and discard the skins from the chiles and transfer them to a small bowl.
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16
Sprinkle with 2 teaspoons of the lime juice, season with salt, and toss to coat; set aside.
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17
When the avocados are ready, use a spoon to scoop out the flesh, place it in a medium bowl, and mash with a fork into rough chunks.
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18
Mix in the cilantro and the remaining 1 tablespoon lime juice.
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19
Taste and season with salt and pepper as needed; set aside.
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20
Remove the pork patties from the refrigerator and lightly season both sides with salt and pepper.
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21
Place the patties on the grill indentation-side up, close the grill, and cook undisturbed ( press down on the patties) until grill marks appear on the bottom, about 5 to 6 minutes.
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22
Using a spatula, flip the burgers, close the grill, and cook until an instant-read thermometer registers 145 degrees F, about 6 minutes more.
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23
Remove to a clean plate and let rest in a warm place or tent loosely with foil for 5 minutes.
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24
Place the toasted buns on a work surface.
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25
Divide the avocado mixture among the bottom buns.
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26
Top each with a patty and a quarter of the chiles and close with a bun top.
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27
Serve immediately.
