Along with some rust, this CJ-2A has all kinds of mods. I’ve unaware of any factor “cowl cover”; that said, the place I’ve seen these cowl extensions most often is in the northern Colorado, Wyoming, and Montana areas, so maybe there was a dealer(s) in those areas offering custom cowl creations? The hardtop looks to be an aftermarket Koenig half cab.
https://bozeman.craigslist.org/pts/d/mc-allister-1947-willys/7487207671.html
“47 Willys ran has 6v system needs new batteries. Has very rare factory cab and cowl cover. Rear pto winch. Great project.”