Heat broiler to 500°. In a medium bowl, toss the carrots with the peanut oil and red pepper flakes. Season with salt and pepper. Transfer to a baking sheet and spread the carrots out into a single layer. Cook until the surface of the carrots is well charred, covered with black blisters, 10 to 12 minutes. Transfer to a bowl.
Immediately add the cheese, honey and lemon juice to the bowl with the carrots, and toss to combine. Let sit for 2 minutes to allow the cheese to melt, then toss to incorporate. Using a slotted spoon, transfer the carrots to a platter, leaving any liquid behind. Serve immediately.