In a large bowl, or the bowl of a stand mixer, dissolve the yeast and 1 tablespoon of the sugar in 1 cup of the water. Let it sit for 5-10 minutes, until bubbling.

Add the oil, egg, salt, and 2 cups of the flour, along with the remaining sugar and water. Beat the mixture until smooth. Continue adding flour until the dough is soft and tacky, but not sticky. (You may need more or less flour.) If using a stand mixer, change to the dough hook and knead until smooth and elastic, about 3-5 minutes. If making by hand, pour the dough out onto a lightly floured surface and knead until smooth, 5-8 minutes.

Place the dough in a greased bowl, turn over to coat, cover, and let rest until doubled, about 45 minutes.

Prepare 2 baking sheets by lining with parchment paper or a silpat liner.

Punch the dough down. Divide the dough into 18 equal sized balls. Roll each of the balls into a long breadstick shape, then place on the prepared baking sheets, making sure to give the breadsticks room to rise. Cover the baking sheets and allow the dough to rise until doubled, about 25-30 minutes.

Heat the oven to 375ºF. Place the baking sheets in the oven and bake until golden brown, 14-16 minutes. If baking both sheets at the same time, rotate halfway through the baking time.

Meanwhile, melt the butter. In another small bowl, combine the parmesan, garlic powder, and salt.

As soon as the breadsticks come out of the oven, brush them with the melted butter, then sprinkle on the parmesan mixture.