In a small microwave-safe bowl, combine the cranberries and apple juice. Cook on high for 1 minute, then stir. Continue to heat for 30 seconds at a time — stirring after each interval — until the apple juice is very hot. Cover and set aside until the mixture is close to room temperature, about 1 hour. Stir in the vanilla and cinnamon. Set aside.
Heat the oven to 375 F. In a large bowl, combine the cornstarch and apple slices. Toss well to coat evenly. Add the cranberries and juice mixture. Mix well. Set aside.
In a large mixing bowl, whish together flour and sugar. Melt butter and add oil. Drizzle butter and oil over dry ingredients. Mixture will be crumbly. Add the ice water 1 tablespoon at a time and mix with a fork until the dough begins to form a rough mass.
Tape a large piece of aluminum foil to the countertop. Sprinkle it with flour. Place the dough in center of the foil and flatten. Using a rolling pin, roll the dough from the center to the edges, making a circle about 13 inches in diameter.
Place the fruit filling in the center of the dough. Spread the filling over the dough, leaving a 1- to 2-inch border. Fold the edges of the crust up and over the filling. The pastry won't completely cover the filling. It should look rustic.
Remove tape from the foil and countertop. Place another piece of foil over the tart to protect the exposed fruit. Slide tart, bottom and top foil included, onto a cookie sheet and bake about 30 minutes. Remove the top foil and continue baking until browned, about 10 minutes.
Cut into 8 wedges and serve immediately.