Preheat oven to 325F and combine chopped pecans, butter and salt in a baking dish, tossing to mix thoroughly.
Bake 10 to 15 minutes, tossing ever 5 minutes, until golden brown.
Let cool in pan.
In a large bowl, whisk together dulce de leche, heavy cream, vodka, vanilla and stevia extract. Sprinkle with xanthan gum and whisk quickly to combine.
Chill 2 to 3 hours.
Churn in an ice cream maker according to manufacturer's directions.
Transfer to an airtight container, stir in salted pecans and press plastic wrap flush to the surface.
Freeze until firm, about 2 more hours
Any leftovers will freeze very solid. Be sure to soften in the refrigerator for half an hour before using.
Ingredients for Dulce De Leche
1 gallon milk
1 vanilla bean
4 1/2 cups white sugar
1 teaspoon baking soda
Instructions for Dulce De Leche
In a large saucepan, bring milk to a boil over medium-high heat. Remove from heat and strain through cheesecloth. Return to pan.
Cut vanilla bean in half and pour the seeds in the milk. Stir in the sugar and replace the pan on medium-high heat, stirring constantly until the sugar is dissolved. Just as the milk mixture begins to boil, stir in the baking soda. Reduce the heat to medium, stirring constantly until mixture thickens. When a wooden spoon drawn through the mixture leaves the bottom of the pan visible, and the mixture is light brown in color, remove the pan from the heat.
Place the pan in an ice bath and stir constantly until dulce de leche is cold. Store in airtight container in refrigerator. Pour into sterile jars, and store in the refrigerator.