Give someone feedback without wrecking the relationship

I need to give feedback to someone on my team, been here two years, I've managed her for six months.

What's happening: In the last three client calls she's talked over the client to correct small details. On Tuesday the client stopped explaining a problem halfway through. Twice I've had to email afterwards to smooth it.
What I want to change: let the client finish, and save corrections for the follow-up email unless it's costing them money
What I'm worried about: she takes any criticism as a sign she's about to be managed out, and she's genuinely good

Before anything else, tell me which part of this is a real problem with consequences, and which part is my preference dressed up as a problem. Be blunt. If it's all preference, say so and I'll drop it.

Then give me:
1. The opening line, word for word. The one sentence that starts the conversation.
2. The two things I have to actually say, with the specific example attached to each. No labels like "constructive feedback", just what I say.
3. The question I ask that lets them talk, and where in the conversation it goes.
4. What to say if they get defensive, and what to say if they agree too fast and nothing changes.
5. What I commit to, so this isn't a list of things they have to fix on their own.

Keep it short enough to read twice before I go in. Write it as speech. No sandwiching the criticism between compliments, that fools nobody.

What you get: An opening line you can say, the two points that matter, and a plan for when it goes sideways.