Crust

To speed things up you can purchase pre-made pie shells in the dairy case at your market or follow these directions to make your own.
Pulse the flour, sugar, and salt together in the bowl of a food processor until combined. Add the butter and pulse until the smallest pieces are about the size of corn kernels, 10 to 12 pulses.Add 5 tablespoons of water and pulse until the dough is no longer dry (when squeezed in your hand, it should form a ball and hold its shape), 4 to 6 times (if the dough is still dry, add another tablespoon or two of ice water). Turn the dough out onto your work surface and form it into a disk.
Wrap the dough in plastic wrap and chill for at least 1 hour or up to 3 days (or freeze for up to 1 month, defrost in the refrigerator overnight before using).

Heat the oven to 325°F.
Remove the dough from the refrigerator (let it sit out at room temperature for 5 minutes to soften). Flour your work surface and roll the dough into a 12-inch circle, 1⁄8 inch thick. Fold the dough into quarters and transfer to a 9½-inch pie plate. Unfold the dough and fit it into the pie plate, then trim off all but 1/4 inch of the overhang. Using your thumb and index finger, pinch the edge of the dough together to form a granny crimp.
Chill while you make the filling. 

Filling

Whisk the egg and the egg yolks together in a large bowl and set aside.
Combine the cane syrup, sugar, cream, and salt in a medium saucepan. Add the butter and melt over medium heat. Once the butter has melted, continue to cook the mixture until it is hot but not bubbling, about 1 minute. Whisk the sugar mixture into the egg yolks a little at a time, just until the bottom of the bowl is warm to the touch, and then add the remaining sugar mixture. Stir in the vanilla and set aside.

Take the pie plate out of the refrigerator. Sprinkle the pecan pieces into the piecrust and pour the filling on top. The photo shows the pecans on top which is the method most often used, we suggest you follow this recipe. Bake until the center has a little resistance, like a soft-setting custard, 30 to 40 minutes. Remove from the oven and cool for at least 1 hour before slicing and serving.

Variation

Bourbon-Chocolate Chip Pecan Pie

Follow the recipe, but add 2 tablespoons of bourbon along with the vanilla to the hot egg-sugar base. Transfer the mixture to a large bowl and place it in an ice-water bath to chill for 8 minutes, stirring occasionally.
Place 1½ cups of pecans into the pie shell and top with an even layer of 1/2 cup of semisweet chocolate chips (or roughly chopped semisweet chocolate).
Pour the slightly cooled filling into the shell and bake according to the recipe.