'milkshake' is a compound noun, or at least Firefox's spell checker doesn't insist on hyphenation.
To 'shake up' is perfectly idiomatic. Using 'up' as a standalone verb is less common and should be your cue.
To 'shake up' is perfectly idiomatic. Using 'up' as a standalone verb is less common and should be your cue.
Like "the old man the boat," the combination makes it hard to parse. The cue is that you get to "the boat" and realize you misinterpreted it. The point was not that it was impossible to understand.