In a large saute pan, melt the butter and then add the brown sugar, salt, and pecans, in that order, with a stir between each. Stir on medium-high as bubbles form, and continue to stir until the sugar is dissolved as much as possible and the coating on the pecans becomes sticky, 6 to 8 minutes. Remove from the heat and spread the mixture onto a baking sheet to cool. Refrigerate for about 10 minutes.
Meanwhile, in a bowl, whisk together the heavy cream, buttermilk, sweetened condensed milk, evaporated milk, and vanilla extract. Use a spatula to release the pecans from the cooled sheet. Add the cooled pecans to the bowl and stir. Make the ice cream one of the following ways:
1. Get fancy and put it in your home ice cream maker and prepare according to the manufacturer's instructions. Place in an air tight 2-quart container and freeze for at least 5 hours, stirring every 30 minutes for the first 2 hours, then every hour for 3 more hours.
2. Add 2 cups ice and 1/2 cup coarse sea salt to a large plastic storage container. Pour the ice cream mixture into a 1-gallon plastic storage bag and seal, squeezing out as much air as possible. Place this bag in the plastic storage container and cover with the lid. Shake vigorously for 10 to 15 minutes. Add more ice and salt if needed halfway through the spin cycle. Depends on your shakin'! Once the shaking is done and you've checked for the right texture for your ice cream, remove the bag from the container and rinse off quickly in cold water. Open and scoop ice cream out, or cut a hole in the corner of the bag and squeeze it out.