Preheat oven to 200ºC on bake.
Whiz beetroot, feta and pine nuts together in a food processor and season with salt and pepper to taste.
Cut pastry into 6 even rectangles. Using a sharp knife, score a rectangle 1cm inside the edge of each piece, making sure not to cut all the way through.
Arrange pastry on a greased baking tray and brush with egg wash. Divide beetroot filling between each galette, and spread to the edges of the inner rectangle.
Bake for approximately 15 minutes until pastry is puffy and golden brown. Remove from oven, garnish with herbs and additional pine nuts, and serve immediately.