Preheat the oven to 375°F. Lightly grease (or line with parchment) two baking sheets.
Place the pecans is a large frying pan over medium heat, swirl the pecans in the pan until they are toasted lightly. As the pecans toast they'll release their oils and you'll be able to smell the aroma of the pecans. Remove them from the heat to cool.
In a large bowl, combine the sugars, butter, shortening, salt,baking soda, vanilla, and vinegar, beat until smooth and creamy.
Beat in the egg until well incorporated. Scrape the bottom and sides of the bowl with a spatula to make sure everything is thoroughly combined.
Mix in the flour, then the chips and toasted nuts. Refrigerate the dough for an hour.
In a small bowl mix the 1/3 cup sugar and salt for the coating. Using your Tablespoon measuring spoon, scoop the dough out and roll into 1 1/2 inch balls more or less. Roll the cookie balls in the sugar/salt coating and place on the prepared cookie sheets with 2" between them.
Bake the cookies for 10 to 11 minutes, they should be light brown on top. Remove from the cookie sheet to a wire rack to cool completely.