Heat up a pan on medium-low heat, and add olive oil and butter.
Lightly salt the fish on both sides.
When the butter has melted, swirl it to mix the oil and butter. Lay the fish steak in the pan, along with the sprigs of rosemary. (You can lay the fish on top of the rosemary.)
After 3-5 minutes depending on the thickness of your fish, check if the side touching the pan is browned. If it is, flip the fish.
Cook the fish for the same amount of time. While cooking, place one of the rosemary sprigs on top of the fish. Then use a spoon to scoop the oil and butter and baste it on the top side of the fish.