Melt butter in a large skillet over medium heat. Add sausage; fry until just beginning to brown, 3 to 5 minutes. Add mushrooms, onion, celery, garlic, and Italian seasoning. Cook and stir until soft, about 10 minutes. Pour mixture into a large bowl; let cool, about 5 minutes.
Stir eggs into the sausage-mushroom mixture. Add bread cubes and 1/2 the chicken stock; stir until stuffing is well combined and moist. Add more chicken stock if necessary.
Preheat a Belgian waffle iron according to manufacturers' instructions. Fill with stuffing mixture; cook until crisp and heated through, about 10 minutes. Repeat with remaining stuffing.