Put the softened butter in the bowl of a stand mixer fitted with a paddle attachment. Whip the butter until it's fluffy. Add the blue cheese, chopped chives, red pepper flakes and ground pepper. Mix until totally combined, scraping the sides as needed.
Lay out a long piece of plastic wrap on top of a piece of aluminum foil and scoop the butter mixture in a long strip down the middle of it. Carefully pull one side of the plastic wrap and foil over the butter, squeezing it gently to form it into a log. Continue to roll the log of butter into a roll. When it's all rolled up, twist the ends (like a piece of candy) until they become very taut (this means the butter is pressing together inside the plastic and foil to form a cohesive roll). Place the roll of butter into the fridge so it will harden, at least 1 hour, or into the freezer if you need to speed along the process.