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I did a little digging in the online OED and came across this in pan, n.1:

III. Extended uses.
14. colloq. (orig. U.S.). A severely critical or dismissive review. In early use freq. in on the pan: (of a person) under reprimand or adverse criticism. Cf. pan v.3 6.

1899 W. J. Kountz Billy Baxter's Lett. 20 She just put everybody in town on the pan and roasted them to a whisper.

The 1899 quotation couples the idea of roasting (giving someone enough heat to almost burn them) and the logical requirement that roasting is done in a pan may be the link you seek.

Emmett