Cab Calloway And His Orchestra:
Cab Calloway (ldr & voc), R.Q. Dickerson, Lammar Wright, Reuben Reeves (tp), De Priest Wheeler, probably Harry White (tb), William Thornton Blue (cl, as), Andrew Brown & Waller "Foots" Thomas (sax), Earres Prince (p), Morris White (bjo), Jimmy Smith (tu), Leroy Maxey (dm).
Thanks, xiphophilos, for your new source. As I do understand the German comments there, I can add that Deutsche Grammphon obviously had a deal with American Brunswick, at least until the early 1930s: German classical music in exchange for US dance music. Thus Deutsche Grammophon was entitled to press records with the original Brunswick matrices. I'll change the country to Germany then.
I'm pretty sure this is NOT a US pressing. I just found a youtube video of Ben Bernie's "Life is just a Bowl of Cherries", Brunswick 6165 from the same year, 1931.
Not only does the label clearly state "MADE IN U.S.A.", it also offers only a Spanish translation.
Please check the latest correction from Belgium to USA (requested by 78rpmfan on Mar 4, 2014: "This is a USA pressing, Belgium never pressed Brunswick 78's.")
This record, however, has German and Spanish translations on the label, something not very characteristic for US records, and the lettering and the print image is more like on German records of the time. So it seems that it was either pressed in Europe (maybe Germany) or in the USA for the European market.
A (blurred) version of the original US label is here (with a barely visible Spanish-only translation for the Middle American market on it).