Combine vanilla sugar, brown sugar, flour and a pinch of kosher salt in a medium bowl, stirring to combine. Add sliced plums, and gently toss to evenly coat. Set aside.

Preheat an oven to 400°F and position a rack in the middle of the oven. Line a baking sheet with parchment paper and set aside.

On a lightly floured work surface, roll out the pastry to a 13-inch diameter circle. You can lightly sprinkle additional flour on the dough, surface and rolling pin if you find the dough is sticking. Rotate the disc occasionally as you roll to make sure the dough is not sticking to the work surface. Transfer the dough to the prepared baking sheet.

Arrange the sliced plums in a series of concentric circles in the center of the crust, leaving a 2-inch border of dough around the edges. Fold the dough up around the filling. Start by folding one edge over the filling. Fold an adjacent edge the same way. There will be a pleat between the two edges. Repeat this process around the entire galette. Dot the exposed fruit with butter bits. Beat the egg yolk and half and half together in a small bowl (egg wash), then brush the edges of the crust with the egg wash mixture. Sprinkle the crust evenly with turbinado sugar.

Bake the galette for 50 - 55 minutes, or until the crust is a deep golden brown. Don't be afraid of color here. Small spots of caramelization = more flavor! Transfer the baking sheet to a cooling rack, and let cool completely on the baking sheet before transferring to a serving platter.