In a 2-quart saucepan over medium heat, add maple syrup and simmer until it reduces to ¾ cup, about 8 minutes (syrup will turn to an orangey color and foam).
Pour in heavy cream and add sea salt. Stir, increase the heat to medium-high and bring to a boil; remove from the heat.
In a medium bowl, whisk egg yolks.
In a very slow stream, temper the eggs with the hot cream mixture, whisking constantly.
Add maple extract to the tempered eggs and whisk again.
Return the cream mixture on the same burner and add the tempered eggs, stirring continuously.
Turn the heat to medium-low, stir constantly, and cook until the mixture starts to boil again, about 2 minutes.
Remove from the heat and transfer the mixture into a large measuring cup.
Let it cool completely stirring once in a while before covering with plastic wrap, making sure it touches the surface to prevent skin formation.
Transfer to the fridge to chill, about 3 hours.
Preheat oven to 350ºF.
Spread walnuts onto a baking sheet lined with a silicone mat or parchment paper and transfer to the preheated oven; toast for 15 minutes.
Remove and cool to room temperature.
When ready to churn, pour chilled custard into the bowl of an ice cream machine and process according to the manufacturers' instructions until it reaches a nice consistency.
About 5 minutes before the end, add toasted walnuts.
Scoop the mixture into a container and transfer to the freezer for 4 hours before serving.