To make the crust, sift the flour, sugar, and salt into a large mixing bowl.
Add the butter and shortening to the flour mixture. Using a pastry cutter, a fork, or your fingers, work in the butter and shortening until the dough resembles coarse crumbs.
Add 2 tablespoons of the ice water and continue to work the dough until it just begins to come together, being careful not to overmix. If the dough seems dry and will not come together into a ball, add the remaining tablespoon of water and work dough just enough to evenly distribute the water.
Transfer the dough to a 9-inch square baking dish and press with your fingertips until the dough completely covers the bottom of the dish and is smooth.
Cover with plastic wrap and transfer the baking dish to the refrigerator; let it rest for at least 1 hour (and up to overnight) before proceeding.
Position rack in center of oven and preheat the oven to 400°F.
Remove the prepared pie dish from the refrigerator. Remove the plastic wrap and, using a fork, lightly prick the pastry all over. This is called "docking."
Cover the pastry with a piece of parchment paper or aluminum foil, fill with pie weights, and bake the pastry for 15 minutes.
Using oven mitts or pot holders, remove the baking dish from the oven and carefully remove the paper and weights. Return the pastry to the oven and continue to bake for another 6 to 8 minutes, or until the pastry is golden brown.
Using oven mitts or pot holders, remove the dish from the oven and transfer to a wire rack to cool completely.
To make the topping, in a medium saucepan, combine the butter, brown sugar, granulated sugar, and honey.
Bring to a boil and cook for 3 minutes. Remove from the heat and stir in the pecans, cream, and vanilla extract.
Pour the topping onto the cooled crust, return the baking dish to the oven, and bake until set, about 15 minutes.
Using oven mitts or pot holders, remove the dish from the oven and transfer to a wire rack to cool. Scatter the chocolate morsels evenly over the top of the hot pecan mixture. Allow to cool completely before cutting into bars.
YIELD: Sixteen 2 1/4-inch squares, serving 12 to 16