Heat 2 tablespoons of oil in a large skillet. and mushrooms and thyme. Season well with salt and pepper. Cook until nearly dry about 10 minutes. Add red wine and cook 3-4 more minutes. Heat 2 tablespoons of oil in large pot. Season stew meat with salt and pepper. Cook meat on high until browned. Add everything except mushrooms and escarole to pot. Bring to boil, then reduce to simmer. Cook until veggies are tender, around 15 minutes. Add mushrooms and escarole and simmer for 10 more minutes.