In a large skillet, heat oil over medium heat. Add onion, and reduce heat to medium-low. Cook, stirring occasionally, until onion rings become very tender and golden brown, 30 to 40 minutes. Remove from heat, and set aside. (This step can be done a day or more ahead; refrigerate caramelized onions until ready to proceed.)
Heat oven to 350°F. Cut squash into 3/4-inch-thick cubes; you should have about 2 1/2 cups total.
In a large bowl, combine squash, onions, orange juice, rosemary, and salt; mix well to combine. Add cheddar, and stir just until evenly distributed.
Place pie crust on a baking sheet. Mound squash mixture in the center, leaving a 2 1/2-inch border of pie crust around the filling. Fold over edges of pie crust to partially cover the vegetable/cheese filling, overlapping crust as needed.
Bake the galette 40 to 50 minutes, or until filling is bubbly and squash pieces are tender. Allow to cool before serving; it’s best to slice the galette when it’s warm, not hot.