1. Adjust oven rack to center position, and heat oven to 275 degrees. Place pie shell in oven if not already warm.
2. Melt butter in medium heatproof bowl set in skillet of water maintained at just below simmer. Remove bowl from skillet, mix in sugar and salt with wooden spoon until butter is absorbed. Beat in eggs, then corn syrup and vanilla. Return bowl to hot water; stir until mixture is shiny and warm to the touch, about 130 degrees. Remove from heat, stir in pecans.
3. Pour mixture into warm shell. Scatter chocolate pieces over pecan mixture. Gently press them into the filling with the back of a wooden spoon.
4. Bake until center feels set yet soft, like gelatin, when gently pressed, 55 to 65 minutes. Transfer pie to rack; let cool completely, at least 4 hours. Serve pie at room temperature or warm, with lightly sweetened whipped cream or vanilla ice cream