Hi Leanne,
Black Star is Mos Def/Talib Kweli/DJ Hi-Tek. I really dig Mos Def, and though I haven't heard the tune you're talking about, he has made quite a few that sound like you describe. He did a collaboration with Ronny Jordan called "Brighter Day" that was cool. His song "Umi Says" is somewhere between rapping and singing and spoken word, and his production is always top notch. Really I would recommend the entire first Black Star album and Mos' solo album Black On Both Sides, they are both as good as hip hop gets. Another track where Mos does his "almost singing" is "Foundation" with DJ Honda.
You may also dig Cee-Lo, check out his album Cee-lo Green and His Perfect Imperfections. Particularly the song "Gettin' Grown" comes to mind. His work with Outkast on the Aquimini album is fantastic, and have a listen to the song "Held Down" with De La Soul where Cee-lo incorporates a gospel sound with hip hop.
Talib Kweli is also worth a listen, the track "Joy" off his latest album is a personal favorite. He did a track with Morcheeba called "Let Me See" that is pretty cool for this rapper with a singer combo.
Common's collaboration with Jill Scott "I Am Music" has a particularly jazzy vibe. Mos Def also has a track with Jill Scott called "Love Rain" that is pretty cool.
Erykah Badu fits right along these lines. Her two studio and one live effort are both outstanding IMO, and she has also worked with Mos Def, Cee-lo, and Outkast.
A whole lot of hip-hop from the early days is jazzy because, well, they sampled jazz. A Tribe Called Quest's The Low End Theory or De La Soul Is Dead are both impossible to go wrong with if you remotely like hip-hop.
The benchmark of all sampling is the Beastie Boys' Paul's Boutique.
Sorry to ramble, hope I helped...