Make the dough for the galette: If making a homemade crust, make the dough at least an hour in advance. Whisk together the flour, sugar, and salt in a large bowl.
Add the cubed butter to the dough and use your hands or a pastry blender to work the butter into the dough until the mixture resembled crumbs, with pieces of butter no bigger than a pea.
Add the sour cream to the mixture and mix in with a fork. Gather the dough into a ball with your hands and flatten into a disk shape. Wrap with plastic wrap and chill for at least an hour (it will need chilling to firm up) before rolling out.
Toss plum slices with sugar, cinnamon, lemon, instant tapioca: In a medium sized bowl, gently toss the plum slices with the sugar, cinnamon, lemon juice, zest, and flour.
Preheat oven to 375°F (190°C). Line baking sheet and roll out dough: Remove the pie dough from the refrigerator to let stand for 5 minutes before rolling out.
Line a baking sheet with parchment paper or a silicone mat, or lightly butter a baking sheet. Lightly flour a clean surface and roll out the pie dough to a 13-inch round of even thickness.
Arrange plum slices in center of dough round, fold up edges: Place rolled-out pie dough in the center of the lined or buttered baking sheet.
Arrange the plum slices in a circular pattern, starting from 1 1/2 to 2 inches from the outside edge of the dough, working your way into the center. Fold the edges of the pie crust up and over so that circle of the filling is visible.
Brush with egg wash, sprinkle with coarse sugar: If you want an attractive finish for the crust, whisk together the egg and cream in a small bowl. Brush on the exposed pastry crust with a pastry brush. Sprinkle with some coarse sugar.
Bake at 375°F (190°C) for 40-50 minutes, until the crust is lightly browned and the filling is bubbly. Cool on a rack for an hour before serving.