My first cold call ever during the first week of 1L, I hadn't read and wasn't prepared. (I figured it would be like syllabus week in undergrad). Anyway, I told the professor, "I apologize but I'm unprepared, can I take a pass?" The professor said "there are no passes, do you have your book with you?" I replied "yes" and then he said something along the lines of "we'll wait for you while you read until you find the answer".... The entire class then sat in silence with me for a long 3-5 minutes while I started reading the case (or at least trying to, who could possibly read with attention to detail under those circumstances) until I found a quote that sounded like it might at least be a good attempt at a wrong answer.

I think the professor's intention was to scare me into never being unprepared again, but in all reality it just made me never afraid to fumble a cold call again (except for in that class) because I knew it would never be as bad as my first one.

My classmates remembered, but in a good way. My group of friends and I all laughed about it the day of graduation about 10 minutes before we walked the stage. None of that bullshit matters, grading is anonymous. You're there to graduate with a JD, not to impress every professor in every class, every semester. Just shake it off and try again.