What can you do with an Armenian cucumber that got this big? You can use it like an uri and make pickles. An uri is a type of melon that people use to make Japanese pickles (tsukemono). Since the actual uri is hard to find in the United States, people sometimes use over-size Armenian cucumbers, because they're similar and actually a melon.
I found two recipes for uri pickles from a cookbook called "Nihon Shoku", a Japanese-American cookbook put together by the Placer Buddhist Church in nearby Penryn, California. The shorter version was called 'uri no kasuzuke', and a longer version that called for a year of curing was called 'uri narazuke'. Both recipes call for sake no kasu, which is a by product of making sake. You can find sake no kasu in a Japanese or other Asian grocery store. Below is the recipe with the shorter curing time.
Uri No Kasuzuke
Uri or cucumber
1 lb. Sake no kasu
1 lb. brown sugar
Cut uri; remove seeds; fill the cavity with salt and leave in shade until salt disappears (about 1 day). Put uri in deep container and put cut side down; place in large flat dish and put weight on. Leave about 2 weeks. Remove from container and lay the uri in the shade to dry, covered with paper for about 2 days. Combine sake no kasu with the brown sugar. Put layer of uri, cut side up, in a container; cover with sake no kasu mixture; repeat, ending with sake no kasu. It will be watery within a week. Taste the uri, if it is too salty, add more sugar. If using pickling cucumber, use whole. It is ready to eat in 2 weeks, but will taste better the linger it stays in the kasu.