Split the squash in half and remove seeds and peel. Slice the squash into 1/2" thick pieces and place in a large bowl. Add the garlic and 1/2 the olive oil. Season with salt and pepper.
Toss until well coated.
Arrange the squash on a sheet pan so that the pieces aren't touching, and roast for about 20-30 minutes. It should be lightly browned on top and well browned on the bottom. Let cool for 15 minutes, then arrange on a plate. Drizzle with Balsamic vinegar reduction. Shave the cheese on top and garnish with a few oregano leaves, then drizzle with the rest of the olive oil.