In a medium mixing bowl, combine minced garlic, mayonnaise, lemon juice, chopped basil, dill, Dijon mustard, kosher salt, and ground black pepper. Mix until smooth.
Preheat the grill to medium-high heat. Pat the salmon fillets dry and rub each with canola oil, kosher salt, and ground black pepper.
Spray the grill grates with nonstick cooking spray. Place the salmon fillets on the grill and cook for about 4 to 6 minutes on each side until they turn opaque and reach an internal temperature of 125°F.
Remove the salmon from the grill and let it rest for about 5 minutes.
Spread herb mayonnaise on both halves of each brioche bun. Layer the butter lettuce on the bottom halves, then add a salmon fillet on top. Cover with the top halves of the buns and serve immediately.
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Notes
Store leftover salmon in an airtight container in the refrigerator for up to 2 days.