½ cup unseasoned rice vinegar
1 tablespoon sugar
1 teaspoon caraway seeds
2 teaspoons kosher salt, plus more
6 garlic cloves, thinly sliced
1 small fennel bulb, thinly sliced on a mandoline, divided
1¼ pounds arctic char or salmon fillet
4 tablespoons olive oil, divided
Freshly ground black pepper
1 tablespoon fresh lemon juice
1 tablespoon chopped preserved lemon peel
½ cup dill fronds
Preheat oven to 300°. Bring vinegar, sugar, caraway seeds, 2 tsp. salt, and ⅓ cup water in a small saucepan to a simmer over medium heat, stirring to dissolve sugar. Remove from heat and add garlic. Let sit until garlic is slightly softened, 10–15 minutes.
Add half of fennel and toss to coat. Let sit until fennel softens slightly and tastes pickled, 8–10 minutes.
Meanwhile, place char in a 2- or 3-qt. baking dish and coat with 1 Tbsp. oil; season with salt and pepper. Roast until flesh easily flakes apart and a paring knife inserted into fish meets no resistance, 15–18 minutes.
Drain fennel mixture; discard liquid. Toss in a small bowl with lemon juice, preserved lemon, remaining 3 Tbsp. oil, and remaining fennel; season with salt and pepper. Mix in dill.
Serve char topped with fennel salad.
Do Ahead: Garlic and fennel can be pickled 1 day ahead. Cover and chill.