Heat oven to 200°C.
In a food processor, combine flour, cornmeal, sugar, and salt. Pulse to combine. Place dry ingredients in a mixing bowl and put the bowl into the refrigerator.
Remove 1/2 stick of butter from the refrigerator and allow it to come to room temperature. In a food processor, add the 1/2 stick of butter to the flour mixture. Pulse until the fat completely disappears.
Add the remaining 1 1/2 sticks butter in separate batches. Pulse until flour mixture resembles the size of a pea.
Combine the apple juice concentrate and the cold water. Using a spray bottle, spritz the dough with the apple juice mixture while folding the mixture with a spatula.
After about three tablespoons of the liquid, check the dough for consistency. It should hold together when compressed but remain relatively dry to the touch. If it does not bind, add a little more water.
Remove from the processor and form the dough into a ball. Wrap the dough in wax paper or parchment paper and rest in refrigerator for 20 minutes.
Heat a cast iron skillet over medium heat. Add pears to the pan and toss for 2 minutes. Add the balsamic vinegar and continue to toss for 30 seconds. Add sugar and cook until the pears have softened.
Add the nutmeg, cinnamon, and the butter and melt slowly. Fold in the blueberries. Remove from heat. Sprinkle on the flour and combine well. Allow to cool to room temperature.
Place dough on a floured piece of parchment and roll out to a 1/4-inch thick disk. Transfer to a baking sheet. Place cubed pound cake in the middle of the dough, leaving a 3-inch margin of crust on all sides.
Spoon filling over the cake cubes and top the pears with 1 ounce of cubed butter. Lift excess crust onto filling and repeat in a clockwise fashion until a top lip has formed around the edge of the whole tart.
Brush the tart with the egg wash and sprinkle the crust with the sugar.
Bake for 30-35 minutes, or until the filling begins to bubble and the crust is golden brown.
Remove from the sheet pan immediately and cool on pie rack.