"..., the old cockroach brain summoning a hankering for a Papaya dog, or two."
I did a few valedictory laps, counterclockwise, as always, then began chopping my way back uphill, the old cockroach brain summoning a hankering for a Papaya dog, or two.
This seems grammatically incorrect. I found it in the New Yorker, and I often see this style in fiction writing. I am curious about what this type of phrase is called. Is it just used for style and rhythm? To me, it feels misplaced. It's referring to the brain of the writer as a young man, but here, it seems like it's referring to "my way back uphill."
Side note: I ask because I'd like to know how to use this structure correctly.