I'm thinking you could set the piece with the holes on top of the peice with the "flatter" designs, then fill it with softened butter. Then chill, and push the pats out with the other designed piece. Just a thought. But I don't know why they would have a design on both sides...it just occured to me, maybe it is a cookie press. Again, why designs on both sides? Hmmm...
I think maybe the way I laid out the pictures is confusing. There are two pieces. The first pic shows them apart, the second is with them together. So when they're together there wouldn't be anywhere to put anything else like softened butter.
The pieces do fit together quite tightly don't they??
I immediately thought of a pastry shell press, but it seems tight for that too. Then I thought of a muslin press. It looks a tad thick for a muslin press, but it could do.....