Preheat the oven to 375 degrees F. Lightly grease a 9x13 inch baking dish.

Heat a large skillet over medium high heat. Add the olive oil, onion, butternut squash and brown sugar. Cook, stirring often until the butternut squash has softened slightly and the onions are fragrant, about 5 minutes. Stir in the mushrooms, and continue to cook until the squash is fork tender (but not mushy) and the mushrooms have caramelized, about 10 minutes. Stir in the garlic, sage, oregano and time. Cook another 30 seconds and then add the balsamic vinegar and season with salt + pepper. Remove from the heat and add the butter. Set aside to cool slightly.

In a very large mixing bowl, whisk together the chicken broth and eggs. Add the bread + Asiago cheese and gently toss to coat. Now add the the butternut squash/mushroom mixture and all the butter to the pan. Gently toss to combine with the bread cubes. Pour the mixture into your prepared baking dish.

Cover the dish with foil and bake for 35-40 minutes. Remove the foil and continue baking for another 10-15 minutes or until the stuffing is golden on top. Serve warm.