In a medium saucepan, combine 2 cups of whole milk and 1 cup of heavy whipping cream. Heat over medium-low until warm, about 5 minutes. In a separate bowl, whisk together 5 egg yolks and 3/4 cup of granulated sugar until pale and slightly thickened. Gradually whisk in the warm milk mixture.

Return the custard mixture to the saucepan over medium heat. Stir constantly with a wooden spoon for about 8-10 minutes until it thickens enough to coat the back of the spoon. Do not let it boil.

Stir in 2 teaspoons of vanilla extract, then transfer the custard to a clean bowl. Cover with plastic wrap, pressing it directly onto the surface. Chill in the refrigerator for at least 4 hours or until completely cold.

In a skillet over medium heat, melt 1/4 cup of butter. Add 1 cup of pecans and sauté for about 5-7 minutes until golden and fragrant. Let cool completely.

Pour the chilled custard mixture into your ice cream maker, following the manufacturer's instructions to churn for about 20-25 minutes until thick.

Gently fold in the cooled, caramelized pecans using a spatula to ensure even distribution.

Transfer the ice cream to an airtight container, smooth the top, and freeze for at least 4 hours until firm.