Most hollyhocks are biennial and don't bloom the first year so you may have something different than what I'm familiar with. Biennial hollyhocks can be trimmed after bloom. I don't know if it helps the plant but the bloom stocks are ugly and the reseeding would be out of control. Keep the new growth that comes up from the roots. I'd be interested to know what kind of hollyhocks you are growing.

I believe I have the summer carnival series...

Here is a picture.

Here is a link that might be useful: Hollyhocks

That's a beautiful hollyhock. I read up on Summer Carnival and it does indeed flower the first year. I don't know if it grows tall and gangly like the hollyhocks I grow. As Ken, our resident curmudgeon says, try pruning it and see what happens. I'm going to try to find seeds of this lovely hollyhock.