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1
To make the hoisin barbecue sauce, heat the oil in a medium saucepan over medium heat.
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2
Add the shallots and garlic and cook until soft, about 2 minutes.
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3
Add the hoisin, ketchup, honey, soy sauce, fish sauce, and vinegar and cook until heated through and slightly thickened, about 10 minutes.
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4
Set aside to cool.
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5
The sauce can be made 1 day in advance, covered, and refrigerated.
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6
Bring to room temperature before using.
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7
To form the burgers, cut the salmon into large pieces and then coarsely chop in a food processor.
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8
Do not overprocess.
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9
(Alternatively you can chop it by hand with a sharp knife.)
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10
Divide the salmon into 4 equal portions (about 6 ounces each).
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11
Form each portion loosely into a 3/4-inch-thick burger and make a deep depression in the center with your thumb.
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12
Place on a plate, cover with plastic wrap, and let chill in the refrigerator for at least 30 minutes before cooking.
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13
Meanwhile, make the slaw.
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14
Heat the oil in a large saute pan over high heat.
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15
Add the ginger and garlic and cook, stirring once, until soft, about 1 minute.
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16
Stir in the cabbage, season with salt and pepper, and cook, stirring once, until slightly wilted, 3 to 4 minutes.
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17
Remove from the heat and stir in the vinegar, sesame oil, and cilantro.
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18
Let sit at room temperature.
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19
To cook the burgers, heat the oil in a saute pan or griddle (nonstick or cast iron) until it begins to shimmer.
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20
Season both sides of each burger with salt and pepper.
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21
Cook the burgers until golden brown on the bottom sides, about 3 minutes.
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22
Turn over, brush with some of the hoisin barbecue sauce, and continue cooking until medium-well, about 3 minutes longer.
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23
Place the burgers on the bun bottoms, drizzle some hoisin barbecue sauce over them, and top with the slaw.
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24
Garnish with pickled ginger, if desired.
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25
Cover with the burger tops and serve immediately.
