Step 1Trim the fronds from the fennel bulbs, finely chop and reserve 2 tablespoons for garnish. Set aside the remaining fronds. Cut away the stalks and the bases from the fennel and quarter the bulbs lengthwise. Cut out the solid core and slice very thin crosswise. This is much better done by hand; a mandoline or slicer will cut the fennel too thin and there won't be any crunch.
Step 2Chop the stalks, fronds and other fennel trimmings into 1- to 2-inch pieces and put them in a medium saucepan along with 6 cups of water, 3 cloves of crushed garlic and 1 tablespoon salt. Bring to a boil and simmer 20 minutes.
Step 3Combine the fennel, olives and walnuts and garlic in a bowl. Add the olive oil, lemon juice, one-fourth teaspoon salt and oregano and toss to combine well. Taste and adjust seasoning. You may need a little more lemon juice or salt.
Step 4Place the halibut in a deep bowl. Pour the hot liquid through a strainer over the halibut and set aside. Carefully turn each piece of fish over after 10 minutes. Let stand 20 more minutes. The outside will be flaky and the center will be set but extremely moist and almost cool. If you prefer a flakier center, leave the fish in the liquid a little longer.
Step 5Place each fillet on a serving plate and mound the fennel salad right beside it. Sprinkle with the reserved chopped fennel fronds. Serve immediately.