I think the right answer is a blend of several here:
1. Talk to your boss about this
Solicit your boss's advice on how to approach this. She may have relevant information and experience that can help here, and you want her awareness and support as you lean into the situation. You don't say if she's responded to any of these cc'd notes; if she has, you may want to talk about why, and whether she should instead work with you to provide a response through you rather than rewarding these informal escalations.
2. Talk to the employee about their behavior
I like to use a "Facts, Impressions, Feelings, and Outcomes" framework for this kind of conversation. It reminds me that, while I may think I know what someone else is thinking, I'm just guessing; the only things that are concrete are behaviors, and that's what we're looking to change here. Walking through this framework forces me to be sure I've got a clear understanding, and that I know what outcomes I'm seeking.
Facts: clear, objective truths. "Sometimes you choose to add my boss to your replies to my email."
Impressions: what you're inferring from the facts. "It seems like you do this when we disagree."
Feelings: how this makes you feel. "When you do that, I don't understand why you've done it. I'm concerned that you're appealing to my boss rather than talking to me."
Outcomes: what you'd like to see happen. "The next time you feel like you want to do this, would you come see me instead? I'd like us to discuss it directly. If we agree that we should escalate it, I'd like us to do that together."
Splitting it up like this, and in this order, gives you the opportunity to understand better each step of the conversation. For example, maybe there's a different pattern you're not seeing ("No, I copy your boss on Thursdays. It just happens that you and I disagree more often on Thursdays"), and understanding that changes your understanding of the situation, your feelings about it, and maybe even the outcome you want.
Finally, if you don't have regular one-on-ones with your team, I'd highly recommend it. They provide exactly the venue for your team to talk about concerns like this, and for you to invest in your relationship with them ... which starts the virtuous cycle where they actively want to talk to you in moments like these.