In a medium saucepan, combine heavy cream and whole milk over medium heat. Stir gently and heat until tiny bubbles form around the edges, about 5 to 6 minutes. Remove from heat.

In a separate bowl, whisk together the egg yolks, granulated sugar, and brown sugar until pale and creamy, about a few minutes.

Slowly pour half of the warm cream mixture into the egg yolk mixture while whisking constantly to temper the eggs. Return the mixture to the saucepan for further cooking.

On low heat, stir the combined mixtures continuously until the custard thickens and coats the back of a spoon, about 5 to 10 minutes.

Strain the custard through a fine mesh strainer into a clean bowl. Add vanilla extract and salt, cover with plastic wrap, and refrigerate for at least 4 hours, or overnight.

Melt unsalted butter in a skillet over medium heat. Add chopped pecans and toast for about 3 to 4 minutes until golden brown. Let cool.

Pour the chilled custard into an ice cream maker and churn according to manufacturer's instructions, usually for around 20 to 25 minutes. Add toasted pecans in the last few minutes.

Transfer the ice cream into a freezer-safe container, spread evenly, and cover tightly. Freeze for at least 4 hours until firm.