Toast the Pecans: Melt two tablespoons of the butter in a small saucepan or skillet over medium heat, then stir in the brown sugar until dissolved.
3 tablespoons unsalted butter, 2 tablespoons brown sugar
Carefully stir one cup of the pecans into the pan to until coated with the butter mixture. Cook until the pecans are fragrant, toasty, and glossy (about four minutes). Remove pecans from heat, transfer them to a heat-safe container, and place in the refrigerator to cool.
1 ½ cup pecans
Make the Ice Cream Base: Add the remaining tablespoon of butter to the same pan and cook it over medium heat until it is golden brown with a toasted, nutty aroma (about two minutes)*, gently stirring every minute or so. Remove from heat and stir the browned butter, vanilla extract, and salt into the sweetened condensed milk until uniform, and set aside at room temperature to cool.*See recipe notes ¾ teaspoon fine sea salt, 2 teaspoons vanilla extract, 14 ounces sweetened condensed milk
Use a stand mixer fitted with the whisk attachment or a hand mixer to beat the heavy cream until fluffy with stiff peaks (about six minutes). Meanwhile, finely chop the remaining pecans.
2 cups heavy cream
Assemble and Freeze: Gently fold the sweetened condensed milk mixture into the whipped cream, followed by the chopped pecans and candied pecans. Spread the mixture into a freezer-safe container, then transfer to the freezer for at least six hours or until solid.
Once frozen, let the ice cream sit at room temperature for a few minutes before scooping, then serve.