I have a couple of Time Electronics Microcal 1030s which could fit your requirements. I bought them secondhand, but to be honest, I think they are way overpriced to buy new as they are basically just a 10 turn pot strapped on to an amplifier. They are actually quite useful to have knocking around on the bench.
I'd guess that Time Electronics also offers a more modern (microcontroller based) version by now. My units are probably decades old (but still available new)
Edit: Oops, re the Microcal 1030, I misread your requirements - it wouldn't really be practical to do 0.05mV resolution @ 110mV, but like I said, might still a useful tool, especially if you want to quickly dial up voltages in the mV range.