Heat the oven to 325 degrees. Place the salmon in a shallow baking dish that fits it with at least 1 inch around all sides. Rub the fillet on the top and bottom with some olive oil then season with salt and pepper.
Place the whole garlic cloves in a small skillet and set over medium-low heat. Cook, turning as each clove lightly blackens in spots, until the cloves are soft and charred all over, 13 to 15 minutes. Transfer the garlic to a cutting board and roughly chop. Sprinkle with 1/2 teaspoon kosher salt then finely chop, using the flat side of the knife to scrape the garlic and salt together as you chop until it forms a sticky paste (or blitz the garlic and salt together in a mini food processor until smooth). Scrape the paste into a bowl, and stir in the mayonnaise, mustard and vinegar. Spread the mayonnaise completely over the top and sides of the salmon.
Bake until the salmon is opaque on the outside and an instant-read thermometer inserted into the thickest part of the fillet reads 120 degrees for medium doneness, 30 to 45 minutes depending on the thickness of the fillet (if you want your salmon just cooked through, take it to 130 degrees).
Remove the pan from the oven and let the salmon rest for 5 minutes. Serve family-style, straight from the baking dish with the side of your choice.
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