In a small bowl, dissolve yeast and sugar in warm water. Let stand until creamy, about 10 minutes.
In a large bowl, mix together the flour and salt. Make a well in the center and pour in the olive oil and yeast mixture.
Mix together until dough forms. Knead dough on a lightly floured surface for 7 to 10 minutes. Place dough in an oiled bowl, cover with a damp cloth, and let rise until doubled in volume, about 1 hour.
Punch down risen dough. On a lightly floured surface, roll out dough into a large rectangle. Cut into strips about 1/2 inch wide by 4 inches long. Place strips on greased baking sheets.
Mix together garlic, butter and Parmesan cheese; brush onto breadsticks. Let rise 20 minutes.
Bake at 375 degrees F (190 degrees C) for 15 minutes or until golden brown.