In a stand mixer bowl, dissolve yeast and 1 tablespoon sugar in a 1 cup warm water. Add the oil, egg, salt, 2 cups of flour and remaining sugar and water. Beat on medium speed with paddle attachment until smooth. Stir in remaining flour, enough to form a soft dough. Using the dough hook attachment, knead the bread on medium speed for 6-7 minutes. Place in a greased bowl, turning once to grease the top. Cover and let the dough rise in a warm place until doubled, which will take about 30-40 minutes. Punch the dough down. Turn it onto a floured surface and divide the dough into about 36 pieces. Shape each piece into a 6-8 inch rope. Place them onto greased baking sheets. Cover and let it rise until doubled, about 25 minutes. Bake at 400 degrees for 10-12 minutes, or until golden brown.
In a small bowl, combine the butter, Parmesan cheese and garlic powder. Brush on the warm breadsticks, or serve it along side the breadsticks.
If the dough is still sticky after adding 5 cups of flour, keep adding flour, a 1/4 a cup at a time, until it forms a soft dough.