Roast Chicken With Oven-Glazed Carrots And Warm Parsley Sauce

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Ingredients

1 whole 3–3 1/2 pounds chicken, giblets reserved for another use, wing tips trimmed
kosher salt and freshly ground black pepper
5 tablespoons olive oil, divided
2 garlic cloves, 1 halved, 1 minced
1 1/4 pounds carrots, peeled, cut into 1-inch chunks
1 teaspoon honey
pinch of cayenne pepper
1/4 cup chopped flat-leaf parsley leaves
zest and juice of 1 lemon