1. Pour equal parts water and sugar in a saucepan and heat until the sugar dissolves, then slightly poach the kumquats in the simple syrup.
2. Whisk an egg in a shallow bowl, dip the salmon fillets in the egg wash, then coat one side with sesame seeds and transfer — sesame-seed side down — to a warm sauté pan with canola oil and bring up to a light heat for a couple of minutes, making sure you don't burn the seeds.
3. Place sauté pan with the fish in a 300-degree oven for five to eight minutes, then put it back on the stove-top, melt 1 tablespoon butter, and use it to baste the fish with the sprigs of rosemary or thyme on top for a couple of minutes.
4. Flip each fillet — sesame-seed side up — onto a plate, next to a portion of sweet potatoes, and spoon some of the vinaigrette sauce around the plate, not directly on the fish.
5. Place some of the poached kumquats on top of each fillet and around the plate, then garnish with basil or mint leaves.