MAKE AHEAD: Microwave or steam the squash up to 3 days in advance. Bake the gingersnap crust up to 1 day in advance. Both should be kept refrigerated.
For the crust
280g (about fifty 3cm cookies) gingersnap cookies, crushed into crumbs (about 2 cups)
5 tablespoons unsalted butter, melted
1/4 teaspoon kosher salt
For the filling
3 large eggs, separated into whites and yolks
1 1/2 cups canned or home-cooked butternut squash puree from one 15-ounce can or a 3-pound squash (see NOTE)
1 cup full-fat coconut milk
1/4 cup maple syrup
2 tablespoons unsalted butter, melted
2 tablespoons white miso
1 tablespoon peeled, grated fresh ginger root
2 teaspoons toasted sesame oil
3/4 teaspoon freshly ground black pepper
1/2 teaspoon kosher salt
For the topping
1 cup plain full-fat or Greek-style yogurt
2 tablespoons toasted/roasted sesame seeds
For the crust: Preheat the oven to 170 degrees. Have a 20 by 33 cm rimmed baking sheet (a.k.a. quarter sheet pan) at hand.
Stir together the cookie crumbs, melted butter and salt in a mixing bowl until the crumbs are thoroughly coated. Press them across the bottom of the baking sheet and slightly up the sides using a metal cup measure or the flat bottom of a glass. Bake for 17 minutes to form the crust, which will darken a bit. Let cool.
For the filling: Increase the oven temperature to 200 degrees.
Place the egg whites in the bowl of a stand mixer (or use a hand mixer, or a balloon whisk and some elbow grease); beat the egg whites on high speed long enough to form stiff, tall, somewhat dry peaks.
Whisk together the egg yolks, butternut squash puree, coconut milk, maple syrup, butter, miso, ginger, toasted sesame oil, pepper and salt in a large, deep bowl, until smooth. Stir in one-third of the beaten egg whites to lighten the mixture, then swiftly and gently fold in the remaining egg whites; it's okay if some white streaks remain.
Use a light touch to spoon the filling evenly over the crust, encouraging it into the corners. It will just fit. Bake (middle rack) for 40 to 45 minutes, until the filling has browned in spots and a knife inserted into the center of the pie comes out clean. Let cool for 10 minutes.
For the topping: Use an offset spatula to gently spread the yogurt over the pie, from corner to corner. Sprinkle the sesame seeds generously across the surface.
Serve warm or at room temperature. Cover and refrigerate any leftovers, then allow them to return to room temperature before serving.
NOTE: To make the butternut squash puree, pierce the entire squash with a sharp paring knife in a dozen places. Place in a microwave-safe dish and microwave on HIGH for 20 to 25 minutes, until a knife plunges easily into the neck of the squash. Let the squash cool, then peel away the skin and scoop out the seeds and strings. Mash the squash until smooth using a potato masher or a sturdy fork. There may be more than what is needed for this recipe; the extra may be stored in the refrigerator for 3 days. Mix it with ricotta and stuff pasta shells, stir it into soups, or add to muffins or scones. No microwave? Roast at 190 degrees on an aluminum-foil-lined baking sheet until fork tender, about 1 hour; then peel, scoop out the seeds and mash.