^That was "The Origin of Batman" from
Batman #47, June 1948. Written by Bill Finger with art by Bob Kane and Charles Paris.
It was also the basis for the
Batman: The Brave and the Bold episode "Chill of the Night!" by Paul Dini, which adapted it (and its sequel revealing the gangster behind Joe Chill) extremely faithfully. It was Diedrich Bader playing Batman rather than Adam West, but West did play Thomas Wayne (along with Julie Newmar as Martha Wayne). It's by far the most intense and dramatic episode of the usually comedic show, and it did a gret job bringing the story to life. (The interesting thing about TB&TB is that it had gone a season and a half without ever showing Batman's face out of costume or clearly identifying him as anything but "Bruce," so when he unmasked and named himself as in the scene above, it was a really powerful, game-changing moment in the context of the series. I wonder if they planned it that way all along.)