Step 1Wash, dry and trim the fennel stalks till they meet the top and sides of the bulb. Remove dry or pulpy outer leaves, stalks and edible leaves. Discard or save the outer leaves and stalks for soup and the leaves for garnish.
Step 2Slice the bulbs thinly crosswise. Place the slices in a large glass or non-reactive bowl with the onion, garlic, lemon and thyme. Mix in vinegar and sugar water. Season with 1 1/2 teaspoons salt and several grinds of pepper and cover with extra-virgin olive oil (or half olive oil, half vegetable oil), making sure that the olive oil covers the fennel.
Step 3Submerge the vegetables using a dish smaller than the circumference of the bowl, weighted with a kettle half-filled with water. Set aside for several hours at room temperature or, if making the day before, place in a tightly closed jar and refrigerate. This makes about 3 quarts marinated fennel, more than is needed for the remainder of the recipe. The salad will keep, covered and refrigerated, for 3 to 5 days; drain the salad before serving.
Step 1Heat the oven to 400 degrees. Arrange the thyme sprigs in single layer in center of a heavy baking sheet. Place the salmon, skin side down, atop the thyme. Season the salmon with half teaspoon salt, or to taste. Spread 2 cups drained marinated fennel (including lemon slices and thyme sprigs) over the fish. Drizzle the oil over the fish. The fish can be prepared up to 8 hours in advance, covered and refrigerated.
Step 2Roast the salmon until the outside of the fish is opaque and the fennel salad is just beginning to caramelize, about 15 minutes. Reduce the oven temperature to 200 degrees and continue to cook until the salmon has reached desired doneness, 5 to 10 minutes. Remove from heat and serve with the remaining marinated fennel.