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Preheat grill to medium.
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Place the sliced zucchini into a bowl with 3 tbsp. olive oil (or more as needed), 1 tsp. kosher salt and ½ tsp. black pepper. Toss to evenly coat the zucchini in the oil and seasonings.
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Mash the minced garlic and ¾ tsp. of the salt on a cutting board (with the side of a chef’s knife or a spoon) until a paste forms. Transfer to a small bowl and stir in the olive oil.
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Check the salmon for any pin bones. Remove and discard any you find. Measure out a piece of heavy-duty aluminum foil (or a double layer of regular foil) large enough for the salmon fillet. Coat the foil with cooking spray. Place the salmon skin-side down on the foil and spread the garlic mixture all over it. Sprinkle the salmon fillet with 1/3 c. basil.
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Transfer the salmon on the foil to the grill. Grill for 10-12 minutes or until the salmon flakes easily and reaches an internal temperature of 145°F. Using two large spatulas, slide the salmon from the foil to a cutting board. Cut the salmon into 4 equal (6 oz.) portions.
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To grill the zucchini, place the slices directly on the grill. Let grill for 5-6 minutes, then flip the slices and grill for an additional 5-6 minutes or until fork-tender. If you want crisscross grill marks, rotate each piece halfway through cooking on both sides.
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To serve, place 1 salmon fillet on each serving plate alongside 1½-2 c. of the grilled zucchini slices. Sprinkle each salmon fillet with a little of the remaining basil and serve.