Never heard of having a special meal on New Year’s Day (or New Year’s Eve.)
It’s only country 51 weeks of the year. Around New Year it can be found just about anywhere. We spent the New Year with the in-laws in Charleston, SC. My Mil made the traditional black-eyed peas (seasoned with hog jowl), collard greens, pork loin and cornbread.
I always have one helping of each, then go back for desert - a big bowl of black-eyed peas with ample amounts of cornbread crumbled into it. Maybe some chopped onion as well. And hot sauce. Mmmmmm.
This was us! 
I started making this when we moved from Vegas to the DFW area. This is one area where I am superstitious (that, and I never put my purse on the floor! :eek:) because we have been fortunate to make it out financially in many stomach churning, sleepless nights situations since we started this tradition.
Missed the cornbread, though…hope that doesn’t disrupt my moolah train! 
Now THAT’S the way to eat black-eyed peas and cornbread! I sometimes like to throw some rice into the mix.
I always do the traditional black-eyed peas and collards both cooked with ham and a little fatback. Cornbread is an absolute must. This year I made a meatloaf. Fried chicken or pork roast are the other two meats I go for on New Year’s Day.
So THAT’S why my family’s not rich–we always missed the collard greens :). Oh well, there’s always next year.