What animal produces these very strange and long edible eggs?

The answer is: Humans! These "long eggs" are produced in a German factory "by extruding cooked egg yolks into a long tube, then covering it with egg whites. [Video below!] One of the first of such machines was called the SANOVO 6-32 a.k.a. the 'long egg machine,'" according to Food & Wine:

Invented in 1974, it was used to make the Danaeg Long Egg, which is still sold today—you can also buy Danaeg Pre-Sliced Long Egg. The Danaeg was not the only mass-produced egg roll to take the 1970s by storm. The Gourm-Egg from Purina Ralston (a one time owner of Jack in the Box) was discussed in a 1977 article from the New York Times entitled "Shell Shocker: Look What They've Done to Eggs."

(via Weird Universe)