you're making a pretty low-quality joke but this headline really shouldn't have made it past the editors' desk in its current form because it's simply too confusing. (Because the term "milk shakes" makes it a garden path sentence.[1])

It's obviously "deliberate" but simply too hard to parse. Personally if I really insisted on the pun I would have put an extraneous comma that disambiguates:

>Controversial New Milk, Shakes Up Big Dairy

That still has the pun in it but at least would be readable. If people wonder why there's an unnecessary comma there they might realize the pun.

[1] https://en.wikipedia.org/wiki/Garden_path_sentence - which includes "When read, the sentence seems ungrammatical, makes almost no sense, and often requires rereading so that its meaning may be fully understood after careful parsing." Certainly true for me.