Preheat oven to 450 degrees. Make a packet for the cod filet using a sheet of foil and drizzle a bit of olive oil on the bottom of the packet.
Pat cod filet dry, season each side with sea salt and black pepper then place in foil packet. Drizzle a little more olive oil over top of filet before sealing packet. Place in oven and bake for about 10 minutes per inch of filet thickness. When cooked, filet will be opaque and glossy, firm to touch, and should flake easily with a fork.
Meanwhile, heat butter in a small saucepan or skillet. After it melts, cook for another minute or so to brown it. Butter should emit a toasty, nutty aroma and you will see solids forming. Add capers and remove from heat.
Pour brown butter and capers over cod filet. Serve with a squeeze of lemon.