While the crust is baking, make the filling. Place the butter, maple syrup, double cream, brown sugar and salt into a small saucepan and place over medium-low heat. Stir every now and then as it heats up, to combine everything.
Once the butter has melted and the sugar has dissolved, increase the heat to medium and bring to the boil. Leave the mixture to boil undisturbed for 3 minutes.
While the mixture is boiling, whisk the egg in a small heatproof bowl, until the white and yolk are completely combined.
Once the filling has boiled, pour it into the egg mixture in a slow, steady stream, whisking constantly to prevent the egg from scrambling.
Add the vanilla extract to the filling mixture and whisk well until the mixture is completely smooth. Finally, stir in the chopped pecans.
By this point, the shortbread base should have finished baking. Pour the warm filling onto the hot crust and level it out with a spatula. Then, place back into the oven and bake for a further 20 minutes, until the filling is just starting to turn a deeper colour around the edges.
Allow the bars to cool completely in the tin before removing and cutting into squares. Serve immediately, or store in an airtight container at room temperature for up to 3 days.