Pour cream into a large bowl and set a mesh strainer over the bowl. Whisk egg yolks together in a separate bowl.
Heat milk, sugar, and corn syrup together in a saucepan over medium-low heat until milk begins to steam, about 5 minutes. Slowly pour about 1/2 cup heated milk into the egg yolks, whisking constantly. Scrape egg yolk mixture into the saucepan with a heatproof spatula.
Cook and stir milk mixture constantly with the spatula, scraping the bottom of the saucepan often, until mixture thickens and coats the spatula, about 10 minutes. Remove saucepan from heat; pour mixture through the mesh strainer into the cream.
Stir 3/4 cup maple syrup, coarse salt, and vanilla into cream mixture, then place the bowl over a larger bowl of ice water; stir to cool to room temperature. Chill mixture in the refrigerator, about 2 hours.
Preheat oven to 275 degrees F (135 degrees C). Spread walnuts onto a baking sheet.
Toast walnuts in the preheated oven until they turn golden brown and become fragrant, about 15 minutes. Set nuts aside to cool to room temperature. Chop nuts coarsely.
Heat the 1/2 cup plus 1 tablespoon maple syrup in a saucepan until it comes to a boil. Stir in walnuts, and return to a boil. Stir nuts for 10 seconds, remove from heat; set aside to cool completely. The nuts will be wet and sticky when cooled.
Remove cream mixture from the refrigerator, pour into your ice cream maker, and freeze according to manufacturer’s instructions. During the last few minutes of churning, stir in wet walnuts.