Let the butter come to room temperature.
Cut off the rind and cut away the pith with a knife. Doing this will expose the juicy flesh of the orange and no bitter chewy bits are added to the compound butter.
For me, the easiest way is to first slice the blood orange in half. This gives you a stable and safe bast to cut away the orange peel.
Next, remove the inner pith of the orange.
Now zest the blood orange peel you just cut off. You only need about 1/4 tsp. (But you can use any amount you like.)
Put all the ingredients into the food processor: trimmed blood orange bits, zest, sugar, and butter in a food processor. I recommend using a small food processor.
Pulse continuously until thoroughly combined.
Check the compound butter for your desired sweetness. I keep it at 2 tbsp for savory dishes and occasionally add additional sugar for my rolls, scones, pancakes, etc.