Bran and Kingship Myths:

The Stark in Winterfell: Bran and the Fisher King Myth

Bran and his Heroic Journey: The Image of the Emperor (2/3 of this work though is also about Arya and Sansa’s heroic journeys)

More about Bran and the Fisher King

Bran and parallels to other Lordly and Monarchical Characters:

Bran’s parallels to his father.

Bran’s parallels to Dany: ASOIAF’s most magical monarchs

Bran and Theon: The Lost Princes

How Bran will return to Winterfell late in TWOW and his role in the War for the Dawn:

The bond between the raven and the wolf: Bran, Arya and the Long Night

Bran and the Caves of Gendel and Gorne

Bran and the Ice Eyes Legend

Other proof for Bran as the Rebuilder:

The Builder was a Greenseer: Winterfell as a magical fusion of Weirwood and Castle, Camelot and Avalon

The Builder’s connection the Last Hero, and Bran’s connection to both

Comparing the Image of the King and the Image of the Shaman in Bran’s Story

My Favorite Thing About Bran