Begin by ensuring your unsalted butter is softened. Leave it out at room temperature for about 30 minutes, or if you're in a hurry, you can microwave it for a few seconds. You want it soft but not melted.
In a mixing bowl, add the softened butter along with the finely chopped black truffle peelings, white truffle oil, and sliced fresh chives. Season with sea salt and pepper to taste.
Using a rubber spatula, mix all the ingredients together until they are well combined. The mixture should be a beautiful blend of creamy butter with flecks of black truffle and bright green chives.
Once everything is mixed, place the butter mixture onto a piece of plastic wrap. Roll it into a log shape, twisting the ends tightly to seal it. This will help maintain its shape when stored.
Place the wrapped truffle butter log in the refrigerator for at least 2 hours to firm up. You can also freeze it if you want to use it later.