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In a small bowl, combine the yeast and 1/2 cup of warm water. Let mixture sit for 10 minutes to dissolve.
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In a large bowl combine the yeast mixture, vegetable oil, sugar, powdered milk, remaining 1 cup of warm water, and 1 cup of flour. Beat for 1 minute on medium speed.
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Switch to a dough hook and add the remaining flour. Knead by machine for 5 minutes, or by hand for 7 minutes. Add 1/2 cup of the shredded cheddar cheese at the end and knead until incorporated. If the dough is sticky, add a little more flour.
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Place dough in a buttered bowl and turn to coat. Cover with a towel and let the dough rise for about an hour, or until doubled.
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Once the dough is rising, melt the butter and stir in the prepared garlic. Cover and set aside to let the flavors combine.
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On a cutting board, chop the remaining 1 cup of shredded cheddar cheese into small pieces. Place in a small bowl, along with the sesame seeds, parmesan cheese, and salt. Add panko bread crumbs, if using. Combine ingredients well. Pour onto a dinner plate.
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Cover 2 large baking sheets with parchment, or generously sprinkle with cornmeal.
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When the dough has doubled, punch it down and divide it in half. Cut each half into 16 pieces.
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Pour the garlic butter on a dinner plate (reheating it if necessary to make it liquid).
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Using both hands, roll each piece of dough into a thin rope about 10 inches long.
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Roll quickly in melted garlic butter and then roll in the sesame seed and cheese mixture.
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Place on prepared baking sheets, fairly close but not touching. Cover and allow to rest while oven preheats.
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Heat oven to 400 F.
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Bake one sheet at a time for approximately 16 minutes, or until golden brown. For a crispier breadstick, let them bake for an additional 2 minutes.
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Cool on a rack.