(although to be clear Askenazim do not genetically look very European compared to most Europeans)
Really depends on who you compare them to.
Naturally American Whites with their predominantly Northern European (German, English, Irish, Scottish) origins aren't really that close to unmixed Askeanazi. But on nearly every study I've run into they are for example closer to Greeks and Italians than the Souther Europeans are to Austrians, British or Russians.
In any case regardless of their genetics, Askenazi Jews are European because:
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
If continuing the discussion becomes impractical, that means you win at open threads; a celebratory top-level post on the topic is traditional.