Thanks to a brilliant Tumblr user, Sherlockspeare, there is an answer to this question. And the combination of Cumberbatch and “Frozen” is completely amazing.
The basic concept takes cut-outs of Cumberbatch as Sherlock from various episodes and inserts them into an animated background. Captions provide the relevant lyrics. If you need some music to go along with the GIFs, please press play on the video above.
Best of all, the combination somehow makes it look like Cumberbatch is actually singing the appropriate words. Yay for mash-ups!