In a small mixing bowl, combine the softened unsalted butter, minced garlic, chopped chives, parsley, and rosemary. Ensure the butter is soft enough to mash and mix easily.
Add the smoked paprika, cayenne pepper, black pepper, and salt to the butter mixture. Stir everything together thoroughly with a rubber spatula or spoon until all ingredients are evenly distributed throughout the butter.
Once well combined, spoon the cowboy butter mixture onto a piece of plastic wrap. Shape it into a log or a compact mound.
Wrap the butter tightly in the plastic wrap, twisting the ends to seal it securely. You can also roll it into a neat log shape for easier slicing later.
Refrigerate the cowboy butter for at least 1 hour to allow it to firm up and the flavors to meld. Once firm, it's ready to be sliced and used.