Printing text between two blank lines

I've been trying to use regular expressions or some kind of counter
thing, but I can't seem to work this right. I have data in a text file
where the im****tant thing I want to extract is between two blank
lines. That's the only systematic way to find the useful lines.

So, it'll go "blank line, im****tant stuff, blank line". There are
plenty of other lines of text that may be have a blank line before or
after it. But only the im****tant ones have both.

Is there a simple way to extract/print these lines? Thanks!