Preheat oven to 425˚F.
Combine EVOO and garlic in a small saucepot. Cook garlic until soft and fragrant, about 5 minutes. Meanwhile, par-roast mushroom caps brushed with garlic oil and seasoned with salt and pepper, cap side down, until just tender, 10 minutes. Cool.
Place the leftover stuffing in a mixing bowl and mix with beaten egg. Stuff the mushroom caps and topped each mushroom with mix of white sharp cheddar, Parm and finely chopped fresh sage. Bake 20 minutes.