Preheat oven to 350 degrees F. Lightly butter a 1 quart baking dish.
In a small bowl, combine bread crumbs, cheddar cheese, and melted butter; set aside for topping.
In a medium-size frying pan over medium-low heat, add olive oil and saute sliced onions, salt, pepper, and 1 teaspoon thyme until onions are lightly browned, approximately 15 minutes. Stir in garlic and cook another minute or so. Remove from heat. Spread onion mixture evenly over the bottom of the prepared baking dish. Set aside the frying pan for later use.
In a large bowl, toss butternut squash cubes with the flour, parmesan cheese, and remaining 1 teaspoon thyme (or to taste) to evenly coat the squash cubes. NOTE: I like to add some additional black pepper at this point. Spread squash mixture evenly over the top of the onions; set aside.
Place frying pan (that you cooked the onions in) over low heat. Add chicken broth or white wine to deglaze, scraping down brown bits from the bottom and sides of the pan, and let simmer approximately 2 to 3 minutes. Remove from head and pour over the top of the squash mixture.
Spread prepared cheese topping over the top of the gratin. Bake for approximately 50 to 60 minutes until the squash is soft and the topping is lightly brown. NOTE: If you find your topping is browning to fast, cover the dish with some aluminum foil.
Remove from oven and let rest for 10 minutes before serving.
Makes 2 to 4 servings.
** Butternut squash is easily found in supermarkets. Beige colored and shaped like a vase or a bell. This is a more watery squash and tastes somewhat similar to sweet potatoes. It has a bulbous end and pale, creamy skin, with a choice, fine-textured, deep-orange flesh with a sweet, nutty flavor. Some people say it is like butterscotch. It weighs from 2 to 5 pounds. The oranger the color, the riper, drier, and sweeter the squash. Butternut is a common squash used in making soup because it tends not to be stringy. Available year-round - peak season lasts from early fall through winter.
Butternut Squash Gratin Recipe: https://whatscookingamerica.net/Vegetables/ButternutSquashGratin.htm