For the brown butter crumble topping: Put the butter in a small saucepan and cook over medium heat until amber brown, 3 to 4 minutes.
Whisk together the flour, granulated sugar, brown sugar, cinnamon, nutmeg and salt in a medium bowl. Stir in the butter. Refrigerate the mixture for 15 minutes, then squeeze it to make crumbles.
For the apple pancake bars: Preheat the oven to 375 degrees F. Line a 9-by-13-inch baking dish with a parchment paper overhang on the long ends and spray with nonstick baking spray.
Whisk together the flour, granulated sugar, baking powder, baking soda and salt in a large bowl. Whisk together the buttermilk, butter, vanilla and eggs in a medium bowl until smooth. Add the wet mixture to the dry along with the granola, lemon zest and juice and apples and mix until just combined. Lumps are ok. Transfer the batter to the prepared baking dish and let it rest for 15 minutes.
Sprinkle the crumble evenly over the batter and bake until lightly golden brown and the top springs back when touched, about 15 minutes. Remove to a baking rack and let cool for 10 minutes.
For the apple syrup: Meanwhile, combine the apple juice, granulated sugar and apples in a shallow skillet, bring to a boil and cook until the mixture is thickened and reduced by half. Add a splash of lemon juice, strain the syrup through a fine strainer and keep warm.
Dust the top of the apple pancake with the confectioners' sugar, cut into bars and transfer to a platter. Drizzle the warm apple syrup over the bars or pass it for dipping.