Preheat oven to 400°. Prepare a baking sheet by lining it with parchment paper, set aside.
Whisk water, oil, sugar, and yeast in a bowl. Allow yeast to proof for 5 minutes, it will turn light and foamy with lots of little bubbles. In a medium sized mixing bowl, sift together flours, parmesan, and salt.
Add yeast mixture into flour, and stir until combined. Quickly knead dough until it comes together.
On a lightly floured surface roll out the dough into a large square approximately 16x16.
Add minced garlic to melted butter and stir, then pour 3/4 of the butter and garlic onto the dough, spread evenly on the dough making sure to cover ever part. Make sure garlic is spread out and not all in one area. Sprinkle the buttered dough with 1/2 cup of parmesan cheese, sprinkling evenly over the buttered surface. Fold dough in half and cut 12 strips, they should be about an inch wide.
Twist breadsticks and place on parchment paper. Repeat with remaining dough. Brush breadsticks with remaining garlic butter then sprinkle with remaining parmesan cheese.
Set in the oven and bake 15-16 minutes. Remove from oven and serve.