I included the shuttle in my original comment. And I agree there have been plenty of restartable engines, that's not the same thing as "throttleable" in my lexicon.....
Throttle is probably a misnomer. They control the rate the fuel pumps work. There are limits the pumps can be slowed to without losing the flame, but they can reduce thrust and do so. The entire launch is configured within those limits.
The Saturn's S-IVB upper stage was fully throttleable. I can't speak to the original Titan upper stage, but the ones flying today are, too.