Combine the oil, garlic and 2 sprigs of sage in a small saucepan. Bring to a simmer over medium-low heat. Cook at a bare simmer until the garlic is soft and lightly browned, about 15 minutes. Set aside to cool. When cooled, strain the oil into a bowl; reserve the garlic but discard the sage.
Preheat the oven to 325 degrees F. Rub a rimmed baking sheet with 2 teaspoons of the garlic-flavored oil and place the salmon skin-side down on the sheet. Rub with 1 tablespoon of the flavored oil and sprinkle with the pink peppercorns, 1 1/2 teaspoons salt and 1/4 teaspoon black pepper. Roast until the salmon is just cooked through, 25 to 30 minutes.
While the salmon cooks, in the bowl of a food processor, combine the chopped sage, parsley and reserved garlic. Pulse a few times until chunky. Add the vinegar, 3/4 teaspoon salt and some pepper. Pulse again to combine. With the motor running, drizzle in the remaining flavored oil through the feed tube. Stop occasionally to scrape down the sides of the processor. The finished pistou should be smooth and bright green; keep processing until the oil looks completely combined. Scrape into a serving bowl.
Divide the salmon into 8 pieces or, to serve it family style, use 2 large spatulas to slide it whole onto a large platter. Serve the salmon with the pistou on the side.
Cook's Note: You can make the pistou several hours ahead and refrigerate. Allow it to come back to room temperature before serving it and stir it well to reincorporate any oil that has separated out.
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