Iron Hearted Violet by Kelly Barnhill

Violet is a princess.  But not in the way princesses are expected to look.  Her eyes are different colors, her hair is wiry and cannot be controlled.  She acts like a tomboy and everyone says she is ugly.  She lives in a world where dragons once roamed, but no more.  Her world is one with a mirrored sky and dragons are afraid of their own image.  She has a friend, the stable master's son.  They have a great time exploring the countryside and the castle itself, which is magical.  Some days rooms that were not there before appear and the two explore them to see what new wonders they can discover.  On one of these explorations, they find a new hallway that leads from room to room, getting smaller after each large space, until they find themselves in a library with a giant picture.  One full of dragons and a single man-like creature who tries to talk to them.  Violet grabs a book, and the two escape from the room.

The King hears of a dragon in the woods near the border of his cousin's kingdom and gathers an expedition to capture and study the dragon.  While he is gone, the Queen, pregnant, dies in childbirth.  Violet, desperate to save her, desperate for her father to return, opens the book she stole from the secret room and reads it.  The next time her friend comes along, she refuses to go with him.  She looks instead into a mirror, hearing the voice of the strange little man, who promises her everything she desires if only she will do one thing for him.  She desires to be a real princess.