Position the rack in the center of the oven and heat to 400°F .
Peel the butternut squash and carefully slice it in half lengthwise. Scrape out the seeds and loose stringy membranes, and cut the squash into 1-inch cubes.
In a bowl, toss the squash with the cinnamon, kosher salt, pepper, and vegetable oil. Spread the squash cubes in a single layer on a large rimmed baking sheet or two smaller baking sheets.
Roast the squash until lightly browned and tender, about 25 to 30 minutes, tossing and flipping every 8 to 10 minutes.
Meanwhile, combine the balsamic vinegar, brown sugar, and the cinnamon stick in a saucepan and bring to a boil over medium-high heat. Reduce the heat to medium-low and cook for about 12 to 18 minutes, stirring occasionally, until it is reduced to 1/3 cup.
Transfer the roasted squash to a serving dish and drizzle with the balsamic glaze.