Start the butter melting in a large, heavy skillet over medium heat.
Quarter the apple and trim out the core, whack each quarter into two pieces (making eighths), and drop them in your food processor with the S-blade in place. Whack each stalk of celery into 4-5 big chunks, and throw them in, too. Quarter the onion, peel, and throw it in, and then dump in the walnuts. Pulse the food processor until everything’s a medium consistency.
Dump this mixture, along with the mushrooms, into the butter in the skillet, turn the heat up to medium-high, and saute everything for a minute or two, stirring. Then cover it, and let it cook for 10 minutes, uncovering every 3 minutes or so to stir the whole thing again.
Stir in the salt and poultry seasoning, let it cook for another minute or two, and serve.