Preheat oven to 400 degrees F. Line a large, rimmed baking sheet with foil and spray with cooking spray.
If the carrots are thick, cut them in half lengthwise; if not, leave whole. Slice the carrots diagonally in 2-inch-thick slices.
Spread carrots in a single layer on the prepared baking sheet. Drizzle with olive oil and toss to coat.
Roast in the oven for 15 minutes.
Meanwhile, whisk together brown sugar, orange juice, and salt in a small bowl until completely combined.
After 15 minutes, remove carrots from the oven. Brush (or drizzle) brown sugar mixture over the carrots; stir to coat, and return to the oven for an additional 10-15 minutes (or until browned and tender). You will not need all of the glaze (probably only 1-2 tablespoons will actually be used), so set aside the extra and drizzle a little bit more over the roasted carrots just before serving.
Season with additional salt, to taste.