Brown butter and vanilla bean add complexity to the apple filling in this rich cobbler.
Preheat oven to 375 degrees. Melt 1/2 stick butter in a small saucepan over medium-low heat and cook, swirling pan occasionally, until butter is golden brown and fragrant, about 8 minutes; let cool. Toss together apples and lemon juice in a large bowl. Combine 1/4 cup flour, 1/2 teaspoon salt, 1/3 cup granulated sugar, brown sugar, and vanilla-bean seeds in another bowl, breaking up clumps and combining with a fork or fingers. Add browned butter to apples. Stir in flour mixture.
Transfer apple mixture to a 9-by-13-inch baking dish, cover tightly with parchment-lined foil. Place a parchment-lined baking sheet on bottom rack of oven to catch juices. Bake apples on middle rack directly over the baking sheet, 10 minutes. Remove and discard parchment-lined foil.
Whisk remaining 2 cups flour, baking powder, 1/2 teaspoon salt, and remaining 1/4 cup granulated sugar in a medium bowl. Cut remaining 1 stick butter into flour mixture using a pastry blender or 2 knives to form clumps that are no larger than small peas. Add cream to flour mixture; stir until a soft, sticky dough forms. Divide dough into 10 equal pieces; arrange over filling. Brush dough with cream, and sprinkle with sanding sugar.
Return cobbler to oven on middle rack directly over the baking sheet until topping is golden brown and juices are bubbling, about 55 to 65 minutes. If topping is browning too quickly, cover loosely with foil. Let cool 20 minutes on a wire rack before serving.