In a heavy-bottomed saucepan, combine 2 cups of heavy cream and 1 cup of whole milk. Heat over medium heat for about 5 to 6 minutes, stirring occasionally, until tiny bubbles start to form around the edges.

In a separate bowl, whisk together 5 egg yolks with ¾ cup of granulated sugar and ¼ cup of brown sugar until pale and creamy. Gradually mix in half of the warm cream mixture.

Return the egg mixture into the saucepan with the remaining cream and cook over low heat, stirring continuously until it thickens enough to coat the back of a spoon.

Strain the custard through a fine mesh strainer into a clean bowl. Stir in 1 tablespoon of vanilla extract and a pinch of salt, then cover and refrigerate for at least 4 hours.

Melt 2 tablespoons of unsalted butter in a skillet and toast 1 cup of chopped pecans for about 3 to 4 minutes until golden and fragrant. Let cool.

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

Transfer the ice cream to a freezer-safe container, cover tightly, and freeze for at least 4 hours to firm up.