Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add pears; cover and steam until tender, 5 to 10 minutes. Transfer pears to a bowl. Add carrots to steamer, cover, and cook until tender, about 10 minutes; add carrots to bowl with pears.
Heat butter in a saucepan over medium heat; stir in brown sugar, honey, cinnamon, and nutmeg. Bring to a simmer, stirring occasionally, until sugar has melted and glaze is slightly reduced, 5 to 10 minutes.
Pour glaze over pears and carrots; toss to coat. Remove pears and carrots with a slotted spoon and transfer to a serving dish; sprinkle with parsley.