How should I store herb butter?
Butter, even a compound butter like this, shouldn't have enough moisture to get moldy easily. I think the issue is that you are clarifying the butter in boiling water, which could be causing pockets of moisture in the finished product. You could try melting the butter in a pan without water, adding the herbs, and then allowing the water based part at the bottom to cook off. Once that has happened, you can strain and chill the butter as usual.