What would you guys recommend as a large frame (as close to full size as possible) 380 pistol.
Everyone has mentioned it already, but Beretta 84FS is certainly at the top. It's rather expensive, however. I see prices around $700, give or take. Beretta tried to discontinue it a few years back, but then put it back into production this year. It remains popular. It is a blowback action and some people do not like the recoil of it.
The P250 was mentioned. Note, however, that I think SiG only made short barrels and short magazines for it. So, while being a chassis design, a 9mm P250 can be easily made as large as you want, a .380 P250 really can't. You're stuck with a gun that kinda looks like a tadpole.
An Erma KGP-68A is not particularly small. However, it can also be expensive, if comes in the original box and with the bluing intact. I saw it selling above $900. An abused example is around $650.
CZ-83 was in service with police. It is about Makarov sized. Also a blowback.
Browning 10/71 is rather large. Blowback again.
Finally, a couple of guns I know nothing about and only seen them in pictures: Bersa BPCC and Girsan MC 14. Either of them are for the police market in the countries that has police still carrying .380s. Both were imported into the U.S., in small quantities.
P.S. I think Llama Especiale is at least BDA sized. However, be careful about not buying one that's too new, e.g. "Max" version. They switched to blowback some time after the III-A version. Up to III-A they had a Browning locked breech.
P.P.S. The Beretta Model 1934 "Corto" was in service with Italian army through the WWII. It is about the size of a Walther, only with a sqared-off grip like on 1914 Berettas. Every time I see one of those, it's in a very poor condition. All of those guns went through a war, so...