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In a small bowl, dissolve the sugar and yeast in the water and let sit for 5 minutes, until top becomes foamy.
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In your stand mixer bowl {or regular large bowl}, combine 2&1/2 cups flour and the salt. Using the paddle attachment {or a good ol' fashioned mixing spoon}, mix the softened butter into the flour until well combined.
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Add the yeast mixture to the flour mixture and use your dough hook and knead for about 8 minutes. Dough may be sticky, so if you need to, add a little bit more flour, until it stops sticking to the sides. Don't add more than 1/2 cup though.
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Place the dough in a covered container and let sit for 1&1/2 hours, until doubled in size.
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Once the dough has doubled, measure out 2 oz. portions of dough and roll each one into sticks that are about 7 inches long.
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Place the dough sticks onto baking sheets and cover and let sit for 1 hour, until doubled in size again.
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Preheat oven to 400ºF.
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Bake the breadsticks for 10 minutes, or until just beginning to lightly brown.
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Combine the melted butter and garlic salt and just after the breadsticks come out of the oven, brush them with the butter mixture, using a pastry brush.