Combine the cranberries, sugar, orange zest, orange juice, and vanilla in a medium saucepan over medium heat. Cook for 5-7 minutes, stirring regularly. Some cranberries will burst. Stir in the apples and continue to cook for 2-3 minutes. Remove from heat and allow to cool slightly. Cover with plastic wrap and refrigerate for at least 30 minutes. (Filling can be made up to 5 days ahead.)
Preheat the oven to 400ºF. Place a baking sheet on the bottom rack and allow it to heat up in the oven.
On a sheet of parchment paper, roll out the galette dough into a 12-inch circle. Spoon a layer of cranberry apple filling into a roughly 8-inch circle at the center of the dough. Carefully turn the edges of the dough over onto the filling. Creases and folds are okay, and will lend a rustic look to the dessert. Extra filling can be added to the center of the galette, if desired. Brush the crust with egg white and dust with turbinado sugar.
With the galette still on the sheet of parchment paper, place it onto the hot baking sheet. Bake for 40-45 minutes, or until golden brown. Cool on a wire rack.
Note: To ensure a crispy crust and prevent a galette with a soggy center, placing the galette onto the hot baking sheet allows the bottom crust to begin baking immediately, creating a flaky crust throughout.