I was explaining this a couple of days ago.
If you are doing it in Illustrator:
Just do a search for "vector halftones" and you should be able to turn a few up.
What you need to do is select the halftone (a gradient in your case) and make sure it's converted to a compound path which will make Ai see it as a single shape and not a group.
Select the parts that you want the halftone to be inside and copy and paste in place so it's in the same position as the original.
Make the parts a compound path as you did with the halftone and then place the halftone where you want it.
Select both and then use your pathfinder window and hit the "intersect" option.
You should now have a halftone pattern that's been cookie cut within the shapes.
It's very important to make the halftone a compound path and the same with the shapes if there is more than one or it won't work.
This is a time-lapse of me doing the same thing at around 1:50.