This ^ you are such a kind professor and they will appreciate your caring approach. For me personally, it helps me to stutter less if the person i am talking to looks me in the eye and doesn’t look away. If you’re worried about the student feeling embarrassed, you might say something like, “i noticed you have a stutter, my family member has a stutter and they told me certain things help and certain things trigger them (like if people ask them to repeat themselves etc), let me know if there is anything i can do to help make you feel comfortable.” I’m sure you’ve got this, it might just help additionally to normalize it a bit.