Place carrots in a medium saucepan. Cover with water. Bring to a boil. Cover, reduce heat, and simmer 10 minutes. Remove carrots with slotted spoon. Drain water. Dry saucepan.
In the same saucepan, add olive oil, honey, garlic, and cayenne. Bring to a boil over med-high heat. Return carrots to pan and cook 5 min longer, stirring constantly, until the sauce caramelizes.