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Preheat the oven to 375°F. Lightly grease (or line with parchment) two baking sheets.
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Place the pecans in a single layer in a pan, and bake until they've darkened a bit and smell toasty, about 8 to 9 minutes. Set them aside to cool, then chop coarsely.
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In a large bowl, combine the sugars, butter, shortening, salt, baking soda, vanilla, flavor, and vinegar, beating until smooth and creamy.
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Beat in the egg, again beating until smooth. Scrape the bottom and sides of the bowl with a spatula to make sure everything is thoroughly combined.
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Mix in the flour, then the chips and toasted nuts.
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If you're going to refrigerate the dough, cover the bowl, and refrigerate for about 4 to 5 hours; or overnight. Cookie dough refrigerated for 3 1/2 to 4 hours will spread moderately; chilled overnight, it will spread much less.
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Mix the 1/3 cup sugar and salt for the coating, and put it in a bowl. Use a spoon (or a tablespoon cookie scoop) to scoop 1 1/2" balls of dough into the sugar/salt mixture, rolling to coat. Then transfer to the prepared baking sheets, leaving 2" between them on all sides; they'll spread quite a bit. Or use a teaspoon cookie scoop to scoop 1 1/4" balls of dough.
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Bake the cookies for 11 to 13 minutes — 11 minutes for smaller cookies, 13 for larger ones. Their edges will be chestnut brown and their tops a lighter golden brown. (For dough that's been refrigerated, add 30 seconds to 1 minute to those baking times.) Remove them from the oven, and cool on the pan until they're set enough to move without breaking. Repeat with the remaining dough.
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Store cookies, well wrapped, at room temperature for several days; freeze for longer storage.
