For the giardiniera chimichurri, combine all the ingredients in a mini-prep food processor and pulse about 10 times until coarse and uniform. Taste and adjust the seasonings with salt and pepper and more vinegar to bump up the acid and to thin out the mixture, if needed. Set aside.
For the barbecue chip dust, in a small bowl, mix all of the ingredients. Set aside 1 tablespoon and store the excess in an airtight container.
For the salmon, sprinkle the fillets all over with the barbecue chip dust, place on a wire rack set in a sheet pan and refrigerate for about 1 hour.
When you're ready to cook the salmon, heat a large nonstick pan over medium heat and add the oil.
Place the salmon in the pan skin-side down and let it sizzle until the skin is golden brown and crispy, 6 to 7 minutes. Gently flip with a fish spatula and let the salmon cook until the flesh is golden brown and the internal temperature is 130°F, 2 to 3 minutes more.
Plate the fish skin-side up and top with the giardiniera chimichurri.
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