In a medium saucepan, combine the butter, vanilla, and 1 teaspoon salt. Cook over medium heat, stirring and watching closely until the butter browns, 8 to 10 minutes. Strain the butter into a medium bowl; cool to room temperature. (Discard solids.)
Preheat the oven to 325 degrees F. Line a 9 by 2-inch cake pan with parchment paper and pack the apples in a dish.
Whisk the yolks and sugar in a large mixing bowl until thick and bright yellow. Gradually whisk in the butter until combined. Stir in the flour and sesame seeds until incorporated. Pour over the apples to cover completely and smooth the top. Bake 20 minutes, then rotate the dish from front to back. Bake 20 to 25 minutes more or until the top is golden and the filling is just set.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.