Add the softened butter, olive tapenade, rosemary, and salt to a food processor. Pulse briefly until all ingredients are incorporated. Season to taste with additional tapenade, rosemary, or salt as desired. The flavors will continue to meld as the butter sits or chills.
Chill the butter, if desired, either in a small bowl or by placing the butter on a piece of parchment paper. Make a round butter log by placing the butter lengthwise on parchment paper, and fold the parchment over the butter lengthwise so it is covered. Then use a cutting board, plate, or another flat object pushed against the butter but on top of the parchment paper at the open end where the two pieces of parchment are. Push the object toward the butter (into the parchment) and it will squeeze into a tube shape. Finish wrapping the parchment around the butter lengthwise and twist the ends. Refrigerate and slice into coins when solid. You can also skip the refrigeration and serve the warm, soft butter in a bowl for easy spreading.
Notes
You can use salted butter instead and skip adding any salt. I prefer to use unsalted butter because I can make it exactly as salty as I want.Amini food processor is perfect to make this butter. You can also use a large food processor or mix the ingredients by hand in a small bowl.Many tapenades have anchovy in them. Keep this vegetarian by using our Vegan Artichoke Olive Tapenade.