In a 12-inch skillet over medium-high, combine the oil, honey, cumin, half of the garlic and ¼ teaspoon pepper. Cook, stirring, until the mixture is fragrant and lightly browned, about 1 minute.
Stir in the carrots, followed by 1¼ cups water and 1 teaspoon salt. Bring to a boil, then cover and cook, stirring once or twice, until the largest carrot pieces are just tender, 8 to 10 minutes.
Uncover the pan. Stir in the remaining garlic, reduce to medium and cook, uncovered and stirring often, until any moisture has evaporated and the carrots begin to sizzle, 2 to 4 minutes.
Off heat, stir in the chili and lemon juice. Let stand for 10 minutes, then stir in the parsley. Taste and season with salt and pepper. Transfer to a serving dish and drizzle with additional oil. Serve warm or at room temperature.
