How to Make It
In a food processor, pulse the 1 1/3 cups of all-purpose flour with the cake flour, cornmeal, baking powder and salt. Add the cream cheese and pulse until the mixture resembles coarse meal. Add the butter and pulse just until the dough is the size of small peas. Sprinkle on the ice water and vinegar and pulse just until a dough begins to form. Turn the dough onto a work surface and knead just until it comes together; roll into an 8-inch log, wrap in plastic and refrigerate until firm, at least 30 minutes.
Preheat the oven to 375°. In a small bowl, combine the granulated, turbinado and light brown sugars; stir in the cinnamon. Cut the chilled dough into 12 slices. On a lightly floured work surface, roll out each slice to a 1/8-inch thickness. Using a 4-inch round biscuit cutter, stamp out 12 rounds. Poke each round several times with a fork, then brush with the beaten egg mixture. Sprinkle the rounds with the cinnamon sugar and transfer to a large nonstick baking sheet. Bake for about 13 minutes, until golden; let cool.
In a saucepan, bring the brown sugar, lime juice, lime zest and orange juice to a boil. Add the blueberries and cook over moderate heat, stirring occasionally, until they begin to pop, about 6 minutes. Transfer the blueberries to a bowl; let cool. Pour the berries into a strainer set over a large bowl and let stand for 30 minutes, until most of the liquid has drained off. Transfer the blueberry juice to a pitcher.
Preheat the oven to 425°. Position a rack 6 inches from the heat source. In a small saucepan, stir 1/2 cup of the sugar with the water over moderate heat until the sugar is dissolved. Cook the syrup without stirring until it reaches 243° to 245° on an instant-read candy thermometer, about 8 minutes. Meanwhile, in a large bowl, beat the egg whites at medium-high speed until frothy. Add the cream of tartar and beat until firm peaks form. Reduce the speed to medium-low and carefully add the sugar syrup in a thin stream. After all of the syrup has been added, add the remaining 1 tablespoon of sugar. Increase the speed to high and beat until the meringue cools to room temperature, about 5 minutes.
Arrange the pastry disks on the baking sheet. Using a slotted spoon, mound the blueberry compote onto the disks. Spoon the meringue onto 6 of the blueberry-topped disks and, using 2 forks, pull the meringue into long spikes. Bake all of the disks for 4 minutes, or until the meringue is golden. Transfer the 6 meringue-less disks to plates. Carefully place a meringue-topped disk on each, drizzle with the blueberry juice and serve.