1. Heat the oven to 400 degrees. Coat a rimmed baking sheet with cooking spray. 2. In a small bowl, toss the shredded carrots with 1 tablespoon of the olive oil, and a pinch each of salt and pepper. Arrange in an even layer on the baking sheet. 3. Peel each apple, then halve it down the center. Use a melon baller to scoop out the core, creating a large cavity at the center of each half. 4. Arrange the apple halves, cut side up, on the prepared baking sheet. If the apples won't rest flat, use a knife to trim the rounded sides just enough to form a flat base. Roast the apples and carrots for 12 to 14 minutes, or until the apples are just tender but not mushy. Remove the carrots from the pan and set aside to cool. 5. Increase the oven to broil. Leave the apples on the baking sheet and sprinkle them with the brown sugar. Broil for 2 minutes. Let cool for 5 minutes. 6. Meanwhile, in a medium bowl, whisk together the remaining 1/4 cup of olive oil, the lemon juice, 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Add the arugula and carrots and toss well to coat. 7. Carefully place each apple half on a serving plate. Mound a quarter of the arugula mixture into each half. Sprikle each salad with blue cheese ans walnuts.
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