Step 1In the bowl of a food processor, pulse the cookies, sugar and salt until sandy in texture, then add the melted butter and pulse a few more times to combine. Turn out the mixture into a buttered 9½-inch deep-dish pie plate, pressing evenly onto the sides and bottom to form a crust with uniform thickness. Freeze the crust and, just before filling and baking, run a pairing knife around the top edge to trim the cookie crust cleanly.
Step 1In a large sauté pan, combine the apples with the sugar, cardamom, seeds and water. Gently simmer until the apples have absorbed the water and are plumped. Remove the apples from the pan and set aside to cool.
Step 1While the apples are cooling, assemble the custard: In a large bowl, whisk together the sugar, flour and salt. Add the eggs and vanilla seeds, and whisk until incorporated. Whisk in the milk until completely combined.
Step 1Heat the oven to 350 degrees.
Step 2If there is any excess liquid with the apples, discard the liquid, and arrange or scatter the apples in the bottom of the prepared crust. Pour the custard over the apples, leaving one-eighth inch of crust at the top.
Step 3Place the pie on the bottom rack of the oven and bake until a light skin forms at the top of the filling, about 5 minutes. Sprinkle the tablespoon of granulated sugar over the filling, then continue to bake until the custard starts to brown on top and a knife inserted into the center comes out clean, 30 to 55 minutes (timing will vary depending on the oven, beginning temperature of the crust and fillings, and type of pie dish). The finished pie will still jiggle slightly when remove from the oven but will set as it cools.
Step 4Cool the pie on a rack, then sprinkle with powdered sugar and serve warm.