Place a rack in middle of oven and preheat to 375°. Place butter in a small saucepan and scrape in vanilla seeds; add pod. Cook over medium heat, stirring often, until butter foams, then browns (be careful not to burn), 5–8 minutes. Remove pan from heat and remove pod.

Roll out dough on a lightly floured surface into a rough 14×10” rectangle about ⅛” thick (alternatively, roll out into a 12” round). Transfer to a parchment-lined baking sheet. Arrange apples & rhubarb on top, overlapping and leaving a 1½” border. Brush fruit with brown butter and sprinkle with sugar. Lift edges of the dough over apples, tucking and overlapping as needed to keep rectangular shape.

Beat egg with 1 tsp. water in a small bowl and brush crust with egg wash. Sprinkle with granulated sugar and bake, rotating once, until the fruit is soft and juicy and crust is golden brown, 40–50 minutes. Let cool slightly on baking sheet before slicing.

Fold in maple syrup into the frozen yoghurt and serve alongside galette.