Really cool! That image in the porcelain is called a lithophane. I see them in sake cups sometimes. Here’s someone who has the same one, but unfortunately doesn’t know much about it either:
That's a really cool piece. Lucky it's not broken...
My first thought was Paul von Hindenburg.
But the older guy on the lithophane doesn't have the classic huge mustache... I can't find a "mature" picture of von Hindenburg with his mustache trimmed like that.
I thought it might be Porfirio Diaz (José de la Cruz Porfirio Díaz Mori), the Mexican general and president of Mexico from 1876-1880 and 1884-1911.
Trouble is, the dude in the portrait has a centre-parting and Diaz seems to be invariably pictured with a side-parting or no parting at all. Same issue with other possibilities.
After re-reading this post I may be wrong. I found the picture that DCMatt posted and went from there. Obviously I went in the wrong direction! None of the older pictures I found of Groener look anything like the one in the mug. So, it's back to the drawing board!
That’s a much better photo of the portrait inside the hat. Maybe a better photo of the hat would help? The front of it appears to have an insignia or symbol in the center of the blue band. If it does, it might help identify the man.
Being designed to be viewed backlit like that doesn’t support my earlier idea of it being an ashtray....
Could it be Ludwig III of Bavaria? But then again after looking at so many Bavarian, Prussian Kings, and Princes they all start to look the same. Also could be that this was a lid off of a beer stein.
Great background information provided by everyone here.
My first thought, was that he looks a lot like by great, great grand-father.
I'm curious as to what this piece's original use might have been for... a paperweight, a tobacco jar lid or based on the glazing, maybe just decorative?
Lithophane beer steins certainly existed as novelty items from the 1830s onwards (plus many later facsimiles/fakes) and in some cases were regimental items. Kaiser Wilhelm sometimes features, but I’m pretty sure that isn’t the Kaiser. However, every one I’ve ever seen has the lithophane in the base of the stein, although I don’t see any reason why there couldn’t be some with the picture in the lid.
This curious item is a stein with a military cap lid similar to the OP’s item but, as is usual, the lithophane is in the base.
It’s in the Mariner’s Museum at Newport, VA and they say that they don’t know much about it apart from:
Made for the American market, it features a naval looking cap (as the lid) with an insignia that is an adaptation of the Great Seal of the United States. The body of the stein also features an insignia used by the US Navy starting about 1870. We know it was produced in Germany because of an impressed number in the bottom, a practice characteristic of the German manufactories; the tell-tale thumb hold on the lid; and the lithophane itself which depicts an obviously German scene.
Lithophane objects of this nature are typically German or Austrian and people tend to focus their search efforts in that direction for an ID. Personally, I believe this piece is American. The insignia on the 'hat' appears to be American and is especially evident on the one in the worthpoint link that randazzo1 provided. I feel this is most likely American General Shafter who was one of the commanding generals during the Spanish-American War. That would also put it in the appropriate time frame for lithophane objects.
Frankly, I've never heard of Shafter. He seems like a notable man in our history.
While doing the research on him I came across this picture:
It shows "old women" pulling down a statue of Shafter, Dewey, and McKinley. The "old women" are labelled with the names of the prominent politicians of the day. Published 1899 in Puck magazine - the first political satire publication.
I only posted this to show that the more things change, the more they stay the same...