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Arrange a rack in the middle of the oven and heat to 425°F.
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Wash, peel and trim the carrots. If they are more than 1-inch thick, cut them in half lengthwise; otherwise, leave them whole. Cut the carrots diagonally into 2-inch-long pieces. Set aside.
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Melt the butter in a small saucepan over medium heat. Continue cooking, stirring occasionally for about 3 minutes. Add the garlic and continue to cook, stirring occasionally, until the butter is light brown, about 30 seconds more. Remove from the heat, add the honey, and whisk to combine.
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Cover your rimmed baking sheet with foil for ease of cleanup.
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Spread the carrots into an even layer on the pan. Drizzle all the sauce over the carrots. Sprinkle with the salt and pepper.
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Roast 15 minutes. Flip the carrots, then roast until the carrots are tender and the edges are charred and crispy, 15 to 20 minutes more.
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Transfer to a serving dish. Finish by sprinkling the toasted sesame seeds over the finished carrots. Serve immediately.