Linguist here, and happy to answer! Unfortunately, the answer is "we aren't really sure." But we have some good guesses.

One popular and seemingly well evidenced theory is that Germanic languages (which both English and German are) originally had a base-12 system. My favorite evidence for this is that in Old English, after you get to sixty, you start prefixing hund-, so hundseofontig for 70, hundeahtatig for 80, hundnigontig for 90, and hundteontig for 100. (Interestingly, in Old Norse, another Germanic language, hundrath meant six-score, or 120. About six-score years ago, it was proposed that Old English functioned similarly, but the Latin Christian influence "shortened" it.) Another accepted etymology for eleven (and elf) is that it is from Proto-Germanic ainlif-, meaning "one left (over ten)." This isn't universally accepted, however.

As for the Romance languages, look to Latin. You'll see that eleven is "undecim" or "1+10" just like you'd hope, and twelve is "duodecim" or "2+10." So how do you get to Spanish once? The intermediate stages are likely lost (Vulgar Latin and Proto-Romance were not written down, by and large), but the processes to get from "undecim" to "once" are well known (although the particular order and processes that Latin > Spanish underwent are debated). You can probably almost hear "once" in "undecim" once you drop the /de/ sound. ("Dozen," incidentally, is a borrowing from Old French based on dozaine < doze < Latin duodecim.)

I might point out that Semitic languages suffer the same issue (eleven and twelve being slightly different than "x + ten").

Edit to correct from French to Old French.