Preheat oven to 425 degrees F (220 degrees C). Grease a rimmed 13x18-inch baking sheet with cooking spray.
Whisk 2 tablespoons olive oil, mustard, and apple cider in a bowl.
Sprinkle chicken breasts with rosemary, 1 teaspoon salt, and 1/4 teaspoon pepper. Place on one side of the baking sheet; brush with mustard mixture. Place butternut squash on the other side of the baking sheet; drizzle with remaining 2 tablespoons olive oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper; toss until well coated.
Roast in the preheated oven until squash is tender and chicken is golden, 35 to 40 minutes. Baste chicken with mustard mixture several times during roasting.