I also have one we just call Broody Hen 'cause that's become her name now.
You basically have 3 options. Well, actually, 4 options.
1) Keep breaking her every time. 2) Give in and let her have some fertile eggs, but only if you're ready to deal with the extra chickens. Luck has it they'll all be cockerels. You could also let her sit on fake eggs for a couple weeks and then give her day old chicks if you can get some this time of year. But raising chicks won't stop her from going broody again later in the summer. So it only solves the problem temporarily. 3) Try to re-home her to someone who really wants to hatch chicks and use her as a momma!
4) Some people will cull a persistently broody hen if she's too much trouble to manage. Sounds like you're fond of her, so probably not your choice, but no judgement if it is. I cull chickens for other reasons and think it's one of the responsibilities of animal ownership.
Wishing you the best. Maybe if you keep breaking her she'll slow down at some point. Post pictures of her babies if you decide to let her have some.