Heat oven to 350 F. Heat a large, oven-safe skillet over medium. Add butter and oil, cooking until butter melts and starts to sizzle. Stir in olives, garlic, and fennel for another minute or so. (If your fish is thinner than 1 inch, cook the olive/butter mixture a few minutes longer.) Carefully place fish fillets in skillet. Spoon some butter mixture on top of each fillet to baste, then transfer skillet to the oven.
Bake until fish is opaque and flaky, 10 to 15 minutes, basting once more halfway through until internal temperature of fish reaches 145 F. Remove from oven. Transfer fillets to serving plates, equally distributing olive/butter mixture. Sprinkle with pepper and fresh dill.
NOTE: Olive varieties that will work well: Castelvetrano, Spanish Manzanilla, Kalamata, Moroccan, or Picholine.
Per serving: 276 calories, 20 grams fat (9 grams saturated fat), 86 milligrams cholesterol, 365 milligrams sodium, 4 grams total carbohydrates, 1 gram fiber, 22 grams protein.
