Set a fine-mesh strainer over a medium bowl, and set the bowl in a larger container of ice water.
In a medium saucepan over medium-heat, heat the milk, cream, ½ cup of the maple syrup and the vanilla- about 5 minutes, until hot. Remove from heat.
In a separate bowl, whisk the egg yolks and the remaining ¼ cup of maple syrup together until smooth. Very slowly whisk about 1 cup of the hot milk mixture into the egg yolks to temper. Then, slowly whisk the tempered egg yolks back into the remaining hot milk. Cook the custard over medium-heat until it is very hot but not simmering and reaching thickness (or 180 to 185℉)- stir constantly.
Strain the custard into the bowl set in the ice bath and let cool, stirring occasionally, for about 10 minutes. Remove the custard bowl from the ice bath, cover tightly with plastic wrap, and refrigerate until completely chilled, about 3 hours (or overnight).
When chilled, stir the custard thoroughly, then pour into your frozen ice cream container. Churn, according to your machine's manufacturer instructions, until the mixture resembles soft-serve ice cream. Add in the toasted walnuts, and churn for 30 seconds until they're mixed in. Transfer the ice cream to a sealed container. Freeze until the ice cream is firm- at least 3 hours.
Notes
How to toast walnuts: In a medium skillet over medium heat, heat walnuts until browned and fragrant, stirring occasionally, about 2 to 5 minutes.