After seeing a similar piece at Whitehall in the Colonial Bedroom, I wanted to learn more about these porcelain tables. I came across this piece, very similar to the side table in question, on 1stDibs. It is a KPM Porcelain Writing Bureau from Germany. They date it from the 19th Century. Apparently it is crafted of porcelain pieces and ebonized wood.
I found other images without provenance or description unfortunately, mostly from auction catalogs past. The first one of Royal Sèvres Manufacture with ebonized wood, ormolu, inset porcelain plates and medallions. The second said only said that it was French. image
This one had the description of having been created by Capodiamonte.
Other bizarre pieces by KPM? How about a porcelain pistol?
In summation, never have I felt like such a Hercule Poirot of antiques yet still coming up short!