Regina Spektor can be rock-ish, but I’m not sure she’s what you’re looking for . . . although her and Ben Folds did a song together, “You Don’t Know Me”.
I’m not sure what HSC is…but A Fine Frenzy, Coldplay, The Hush Sound, Regina Spektor Eleisha Eagle, The Fray, Sara Bareilles, Norah Jones (although she’s more jazz), and Ingrid Michaelson (in some songs)