Melt butter in a large, heavy pot over medium heat. Add the onions, carrots and celery and cook until soft, about 10 minutes. Carrots will still be a little hard, that’s a good thing.
Toss the pork in just enough cornstarch to coat. Then place in the pot with the vegetables and brown on all sides as best as you can.
Add in the chicken and beef broths, sage, savory herb and salt and pepper to taste.
Cook on high heat for 5 minutes, then reduce to medium-low heat and let it cook down for about 2 hours.
Add the potato and cook, uncovered, for 15 minutes. Then add the Brussels sprouts and cook an additional 15 minutes.
Add the apples and cook for another 10 minutes, they will stay a little crunchy.
Test the thickness of the sauce, it should coat the back of a spoon. If you want it thicker, stir in a little cornstarch with beef broth while still on the heat.