In a medium saucepan, combine heavy cream and whole milk over medium heat, stirring until small bubbles form around the edges, about 5-6 minutes.

Whisk together the egg yolks, granulated sugar, and brown sugar in a separate bowl until light and creamy, about 2 minutes.

Slowly pour half of the cream mixture into the egg mixture while whisking continuously to temper the eggs.

Return the tempered mixture to the saucepan and cook over low heat, stirring until it thickens and coats the back of the spoon, about 5-7 minutes.

Strain the custard through a fine mesh sieve into a clean bowl, stir in the vanilla extract and salt, then chill for at least 4 hours.

Melt unsalted butter in a skillet over medium heat, add the chopped pecans and toast for 3-4 minutes until golden brown.

Pour the chilled custard into an ice cream maker and churn according to the manufacturer's instructions, about 20-25 minutes.

Add the toasted pecans in the last few minutes of churning, then transfer to a freezer-safe container and freeze for at least 4 hours before serving.