Warm the Cream and Milk: In a medium saucepan, combine the heavy cream and whole milk. Heat over medium heat, stirring occasionally, until the liquid is just about to simmer—small bubbles should form around the edges, but do not let it boil.
Whisk Egg Yolks and Sugars: While the cream mixture is heating, whisk together the egg yolks, granulated sugar, and brown sugar in a mixing bowl until the mixture is smooth, pale, and slightly thickened.
Temper the Eggs: Gradually ladle about ½ cup of the warm cream mixture into the yolks while whisking constantly. Add another 1 cup of the warm cream in small increments, continuing to whisk to avoid scrambling the eggs.
Cook the Custard: Return the tempered egg mixture to the saucepan with the remaining cream. Cook over medium heat, stirring slowly and consistently with a rubber spatula or wooden spoon, until the mixture thickens enough to coat the back of a spoon—about 5–6 minutes.
Strain and Cool: Pour the hot custard through a fine mesh strainer into a clean bowl to remove any bits of cooked egg. Stir in the vanilla extract and salt. Nest this bowl in an ice bath and let it cool for about 10 minutes, stirring occasionally. Then cover and refrigerate for at least 2 hours or until thoroughly chilled.
Toast the Pecans: In a small sauté pan over medium heat, melt the butter. Add the chopped pecans and salt. Stir frequently for 3–5 minutes, or until the nuts are golden and fragrant. Be careful not to burn them. Once toasted, transfer the pecans to a paper towel-lined plate to cool. Discard excess butter or reserve for another use.
Churn the Ice Cream: Pour the chilled custard into your ice cream maker and churn according to the manufacturer’s instructions—typically around 25–30 minutes, or until it reaches a soft-serve consistency.
Mix in the Pecans: With the machine still running, add the cooled pecans during the final 5 minutes of churning, allowing them to fully incorporate into the ice cream base.
Freeze Until Firm: Transfer the ice cream to a freezer-safe container (such as a loaf pan). Smooth the top, cover with plastic wrap or foil, and freeze for at least 6 hours, or overnight, until the ice cream is scoopable and firm.