Preheat the oven at 400 degrees F. In an ovenproof dish, coat the bottom with olive oil so the fish doesn't stick. Sprinkle salt and pepper over the fish. Once oven is preheated, add the fish to the oven and bake for 15 minutes.

While fish is baking, melt the butter in a small saucepan over medium-low heat. Add the shallot and cook 3-5 minutes, stirring occasionally. Do not let shallot burn.

Remove from the heat, add the parsley, lemon zest, and thyme sprigs. Stir to combine, then let sit for 5 minutes. Remove thyme leaves.

Once fish is done, let rest for 2-3 minutes, then spoon the herb butter sauce over the fish. Sprinkle with more salt and pepper. Serve with lemon halves, if desired.