In a medium bowl, beat the butter with an electric mixer until pale and creamy, about 3 minutes. Gradually beat in the sugar until well blended.
In a small bowl, whisk the egg yolk with the maple syrup and vanilla. Drizzle the egg-yolk mixture into the butter, beating at low speed until incorporated.
Using a wooden spoon, stir in the flour and pecans. Divide the dough in half and shape into 2 disks. Wrap each disk in plastic and refrigerate until chilled, at least 2 hours or overnight. Let the dough stand at room temperature for 10 minutes before rolling it out.
Preheat the oven to 325°. Roll out each disk of dough 1/4 inch thick between 2 sheets of wax paper. Cut the dough into 2-inch rounds and transfer to baking sheets lined with parchment paper. Bake for 20 to 25 minutes, or until golden. Transfer the cookies to wire racks to cool.
The dough can be frozen for up to 1 month. The cookies will keep for up to 1 week in tightly sealed tins.