In a small bowl, stir together the sugar and water. Sprinkle top with yeast and let stand until foamy, about 10 minutes. Stir in vegetable oil.

In a large bowl, whisk together flour and salt. Make a well in the center and add yeast mixture; stir to combine. Using dough hook, knead dough on medium speed until smooth and elastic, about 3 minutes (OR, knead by hand on a lightly floured surface until smooth and elastic, about 5 minutes). Shape dough into a ball and transfer to a lightly greased bowl; turn to coat. Cover bowl with plastic wrap and let rise in a warm place until doubled, about 1 hour to 1 hour, 30 minutes.

When dough is risen, heat oven to 450 degrees F. Place an inverted baking sheet on the middle rack. Line a second baking sheet with parchment paper; sprinkle with cornmeal. In a medium bowl, toss together cheeses, garlic powder, salt and parsley flakes. Divide dough in half; press each piece on the cornmeal-covered parchment paper into an 8-inch square. Top one side of each square with 1/2 cup (for each) of the cheese mixture. Fold over and press edges lightly to seal. Use a sharp knife to slice dough into 8 1-inch strips, stopping just before the folded edge. Sprinkle evenly with remaining cheese mixture.

Carefully slide dough on parchment paper on top of inverted baking sheet in oven. Bake until golden brown and bubbling, about 12 to 15 minutes. Let cool slightly before pulling apart into breadsticks.