Preheat the oven to 400°F (200°C). Toss the butternut squash cubes with a tablespoon of olive oil, half the sage, and a pinch of salt. Spread them evenly on a baking sheet and roast for about 25-30 minutes until tender and slightly caramelized, smelling warm and nutty.
While the squash roasts, heat a tablespoon of olive oil in a large skillet over medium heat. Add the diced onion and cook until translucent and fragrant, about 3-4 minutes, stirring occasionally. Then, add the minced garlic and cook for another minute until it becomes aromatic.
Stir in the chicken pieces and season with salt and a pinch of sage. Cook for 5-7 minutes, turning occasionally, until the chicken is golden and cooked through, with a firm texture. Pour in the chicken broth, scraping up any browned bits from the bottom of the skillet, and simmer for 5 minutes until slightly reduced.
Once the butternut squash is done roasting, gently fold it into the chicken mixture, combining everything evenly. Transfer this mixture into a greased casserole dish, spreading it out to a uniform layer.
Sprinkle the shredded cheese evenly over the top of the casserole. Place the dish in the oven and bake for 15-20 minutes until bubbling and golden around the edges, with the cheese melted delightfully.
Remove the casserole from the oven and let it rest for a few minutes. The aroma of toasted sage and caramelized squash will be inviting; it will also help the dish set slightly, making it easier to serve.
Serve the casserole warm, scooping out generous portions that show off the hearty chunks of squash and tender chicken beneath the melted cheese layer. Enjoy the cozy, flavorful bite with your favorite sides.