I don't think the solution here is to make your partner stop talking, because from my point of view, if you want him/her to stop talking, just stop, stop everything not just talking.
The alternative correct solution would be trying to talk about somethings else doesn't sound boring, something new, new experiences.
And if you have nothing new to talk about, so this is another problem, and the solution is to go and do something new right now, do something new by yourself to be happy to start talking about, do something new with her/him.
Another solution is sharing some activities, sport, reading, video games, watching movies (I used to go to cinema weekly for example).
One more solution is asking for her/his opinion on certain subjects which you find not boring.
I am sure there are too many other solution rather than just STOP