The Edge of Forever: Episode 19
 
Kirk, Spock, and Dr. McCoy meet a regenerated Zefram Cochrane and his gaseous companion ("Metamorphosis"). Spock deals with daddy issues, Kirk is stabbed in the back, and The Enterprise comes under attack all while delivering delegates to a conference ("Journey to Babel"). And the show closes with Dan and Mike discussing more Doctor Who / Star Trek crossovers because Dan and Mike.