Arrange a rack in upper third of oven; preheat to 425º. In a large skillet over medium-low heat, cook garlic, rosemary, honey, orange juice, oil, butter, salt, and pepper, stirring occasionally, until butter is melted, about 5 minutes (Sauce will have thickened slightly.). Remove from heat; discard garlic and rosemary.
Add carrots to sauce and toss to coat. Transfer carrots to a parchment-lined baking sheet, arranging in a single layer.
Roast carrots, tossing halfway through, until fork-tender, 20 to 23 minutes.
Transfer sheet to a wire rack and let cool 2 to 3 minutes. Top with parsley and a little more salt.
