Transfer the crust. Carefully move the rolled dough onto the parchment-lined baking sheet before adding the filling.
Create a moisture barrier. Sprinkle the 3 tablespoons flour evenly over the center of the dough, leaving a 2-inch (5 cm) border around the edge. This helps absorb the plum juices as the galette bakes.
Arrange the plums. Layer the sliced plums over the floured portion of the dough, keeping the outer border uncovered.
Season the fruit. Combine ¼ cup of the sugar with the cinnamon, cardamom, and fresh thyme. Sprinkle evenly over the plums.
Add the butter. Scatter the cold butter cubes over the fruit.
Fold the crust. Fold the exposed dough up and over the outer edge of the plums, pleating the dough as you work around the galette. Leave the center open.
Finish the crust. Brush the folded pastry lightly with milk. Sprinkle the remaining 1 tablespoon sugar over the crust.
Bake until deeply golden. Bake for about 35 minutes, until the crust is crisp and golden brown and the plum juices are bubbling in the center.
Cool before slicing. Let the galette cool on the baking sheet for about 30 minutes. This gives the plum juices time to thicken slightly before serving.
Serve. Enjoy warm or at room temperature, as is, with softly whipped cream, or with a scoop of vanilla ice cream.