Melt butter in heatproof bowl set in skillet of water maintained at just below simmer. Remove bowl from skillet and stir in sugar and salt until butter is absorbed. Whisk in eggs, then corn syrup and vanilla until smooth. Return bowl to hot water and stir until mixture is shiny, hot to touch, and registers 130 F. Off heat, stir in pecans.
Pour pecan mixture into warm pie crust. Bake pie until filling looks set but yields when gently pressed with back of spoon, 50 minutes to 1 hour. Let pie cool on wire rack until filling has firmed up, about 2 hours; serve slightly warm (see note) or at room temperature.
Basic Single-Crust Pie Dough
We wanted pie dough that we could count on for reliably flaky, flavorful, crust and achieving it came down to determining the right fat, the right proportion of fat to flour, and the right method for combining them. A proportion of 3 parts butter to 2 parts shortening proved optimal for both flavor and texture, and a high-fat ratio of 2 parts flour to 1 part fat produced a workable, tender dough.
Makes enough for one 9-inch pie. Total time: 30 minutes (plus 1 hour for chilling)
1 1/4 cups (6 1/4 ounces) all-purpose flour
1 tablespoon sugar
1/2 teaspoon salt
3 tablespoons vegetable shortening, cut into 1/2-inch pieces and chilled
5 tablespoons unsalted butter, cut into 1/4-inch pieces and chilled
4-6 tablespoons ice water
Process flour, sugar, and salt in food processor until combined. Scatter shortening over top and process until mixture resembles coarse cornmeal, about 10 seconds. Scatter butter pieces over top and pulse until mixture resembles coarse crumbs, about 10 pulses. Transfer mixture to medium bowl.