In the meantime, preheat oven to 375°. Line a large cookie sheet with parchment paper. Flour paper lightly. Flour a rolling pin and roll dough into a 10-inch circle on the parchment paper. If dough cracks, press it back together with fingertips. Fold the edge of free-form crust inward 3/4 inch and press gently to form a rim. Evenly prick bottom with a fork. Refrigerate dough 15 minutes. Bake until golden brown, 12 to 15 minutes.
Crumble goat cheese evenly over bottom of crust. Arrange plums in concentric circles over goat cheese. Drizzle with 2 tablespoons honey. Bake 15 more minutes, or until plums soften slightly and crust is further browned on bottom. Remove from oven, drizzle with remaining honey and place on a rack to cool. Serve warm or at room temperature.