Put the flour, sugar and salt in a food processor fitted with a metal blade and pulse to combine. Add about a third of the chilled butter cubes and process until the butter is absorbed. Add the remaining butter and pulse until the butter is the size of peas, 5 or 6 pulses. Add the vinegar. Then, while pulsing quickly a few times, add the ice water through the tube. Squeeze some dough between your fingers; it should just hold its shape without feeling wet. If it is crumbly, add more ice water a tablespoon at a time. Pulse quickly; do not overwork the dough or the crust will be tough. Wrap the dough loosely in a large piece of plastic wrap, then firmly press and flatten it into a thin round. Refrigerate for 1 hour.
Lightly dust a work surface with flour, then roll the dough into an 11- to 12-inch round, about 1/8 inch thick. Center the dough in a 9-inch pie plate, with an even overhang all around. Fold the edges and flute or crimp. Chill for at least 30 minutes.
Preheat the oven to 375 degrees F.
Press a piece of foil over the chilled crust, then fill with pie weights, raw beans or rice. Bake to set the crust, about 20 minutes. Remove the foil and weights and bake until the crust is light brown, 5 to 10 minutes more. Let cool slightly before adding the filling.
For the filling: Sprinkle the shallot evenly into the crust. Put the Gouda, chicken and spinach in a medium bowl and toss to combine. Sprinkle it in an even layer over the shallots.
For the custard:
Whisk together the half-and-half, eggs, 1/2 teaspoon salt and 1/4 teaspoon pepper in a medium bowl.
Pour the custard over the filling. Lower the oven temperature to 350 degrees F and bake until set, 35 to 50 minutes. Let cool at least 30 minutes before serving warm or at room temperature.
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