The day before you plan to make the dessert, combine the flours, salt, and 2 tablespoons of the sugar in a mixer fitted with a dough hook. Dissolve the yeast in the water. With the mixer running at low speed, add the yeast mixture to the flour mixture. Add the eggs and mix well. Add the butter and mix at medium speed until smooth, about 10 minutes. Transfer to a bowl and cover tightly with plastic wrap. Refrigerate overnight.
The next day, turn the dough out onto a floured work surface. Roll dough into a 9 by 13-inch rectangle, about 1/2-inch thick. Place on a sheet pan. Loosely drape plastic wrap over the dough and let rise in a warm place until doubled in bulk, 1 to 2 hours.
Preheat the oven to 350 degrees. Remove the plastic wrap from the brioche dough and sprinkle with the remaining 2 tablespoons sugar. Bake until golden brown, 15 to 20 minutes. After 10 minutes, rotate the pan to ensure even cooking. When baked, immediately remove to a wire rack and let cool to room temperature.
Vanilla Custard: In a medium saucepan, heat the milk and vanilla bean to a boil over medium heat. Immediately turn off the heat and set aside to infuse for 10 minutes. In a bowl, whisk the egg yolks and sugar until light and fluffy. Add the cornstarch and whisk vigorously until no lumps remain. Whisk in 1/4 cup of the hot milk mixture until incorporated. Whisk in the remaining hot milk mixture, reserving the empty saucepan. Pour the mixture through a strainer back into the saucepan. Cook over medium-high heat, whisking constantly, until thickened and slowly boiling. Remove from the heat and stir in the butter. Let cool slightly. Cover with plastic wrap, lightly pressing the plastic against the surface to prevent a skin from forming. Chill at least 2 hours or until ready to serve. (The custard can be made up to 48 hours in advance.)
With a serrated knife, slice the sheet of brioche in half lengthwise. Spread the bottom and top generously with custard. Place washed and dried rose petals over the custard, covering the surface entirely. Place the top brioche on and press lightly. With a serrated knife, cut into finger sandwiches, discarding the edges.