For the crust: Cream the butter and granulated sugar in a stand mixer, beating until light and fluffy. Beat in the eggs, milk, and vanilla until combined.
Whisk together the flour, baking powder and salt in a separate bowl. Add the flour to the mixer in 2 additions. Mix until the dough comes away from the sides of the bowl. Form the dough into a disc and wrap with plastic wrap. Refrigerate for at least 30 minutes and up to 1 day to chill.
For the filling: Meanwhile, combine the half-and-half, granulated sugar, cornstarch, lemon zest, vanilla bean seeds and salt in a saucepan. Bring slowly to a boil, then simmer, whisking, until the mixture thickens, about 2 minutes. Remove from heat and allow to cool for a few minutes, then press a sheet of plastic wrap against the top of the mixture to keep a skin from forming. Cool completely.
For the apples: Preheat a grill for cooking over medium heat.
Put apple quarters in a bowl. Drizzle with the butter and light brown sugar and toss.
Grill the apple quarters until lightly caramelized, 3 to 4 minutes per side. Allow to cool briefly, then thinly slice lengthwise.
For the assembly: Preheat the oven to 350 degrees F.
Remove the dough from the refrigerator and let sit for 5 minutes at room temperature to remove the chill so it's easier to roll.
Lightly flour your workspace and roll out the dough to 1/4-inch thick, then carefully place in a deep-dish pie pan. Trim the edges, then crimp. Whisk the cooled filling until smooth, then pour into the shell.
Bake the pie until the crust is golden brown (the custard filling will still be jiggly), 30 to 35 minutes. Let cool completely, then refrigerate until well chilled and the filling is set, 2 to 4 hours. Top the pie with sliced apples, a big drizzle of honey and powdered sugar.
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