Preheat oven to 350 degrees F. If using homemade pate brisee, lightly dust a clean work surface with flour, and roll dough into a 12-inch circle. Fit circle into a 9-inch pie plate being careful not to stretch dough too thin; create edges of choice. Transfer to freezer until firm, about 15 minutes.
Coarsely chop 1 1/4 cups pecans; set aside. In a medium bowl, combine eggs and sugar. Whisk to combine. Add corn syrups and vanilla. Whisk until well combined. Add chopped pecans, and stir. Pour into prepared crust.
Arrange remaining 1 1/4 cups pecan halves decoratively on top of pie. Bake until crust is golden, filling is firm, and a cake tester inserted in center of pie comes out clean; 50 to 55 minutes. Cool completely before slicing. Serve with whipped cream.
In the bowl of a food processor, combine flour, salt, and sugar. Add butter, and process until the mixture resembles coarse meal, 8 to 10 seconds. With machine running, add ice water in a slow, steady stream through feed tube. Pulse until dough holds together without being wet or sticky; be careful not to process more than 30 seconds. To test, squeeze a small amount together: If it is crumbly, add more ice water, 1 tablespoon at a time. Divide dough into 2 equal balls. Flatten each ball into a disk, and wrap in plastic. Transfer to the refrigerator, and chill at least 1 hour. Dough may be stored, frozen, up to 1 month.
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