Heat oil in a large skillet, preferably castiron, over medium-high heat until beginningto smoke. Cook halibut until goldenbrown, 6–8 minutes. Turn and cook untilother side of fish is golden brown, about4 minutes longer.
Add butter, thyme sprigs, and garlicto pan and cook, tilting pan and spooningbutter over fish, until halibut is opaquethroughout and butter is brown, about2 minutes.
Add capers; toss in butter towarm through.
Divide halibut among plates and spoonbutter sauce over.