Prepare a baking sheet by spraying with a non stick cooking spray. Set aside.
In a large bowl, stir yeast, oil, and sugar into warm water.
Let bloom for 10 minutes or until mixture becomes foamy.
Next, whisk in egg and salt.
Slowly add flour until a smooth dough forms.
Roll dough into a ball and place in a greased bowl. Let rise for about an hour, or until dough has doubled in size.
Preheat oven to 425°.
Next, transfer dough onto a well floured surface and knead until smooth and all of the air is out of the dough. Form back into a ball.
Using a dough cutter, or knife, divide dough into 12 pieces.
Now, roll each piece of dough into a ball and then roll out to desired length (approximetly 5 to 6 inches long.)
Place breadsticks onto prepared baking dish and let rise for 10 minutes.
Place breadsticks into oven and bake for 8-10 minutes or until golden brown.
While breadsticks are baking, prepare your parmesan garlic butter.
In a small, heat-safe bowl, melt butter in microwave and heat for 30-45 seconds.
Next, add parmesan cheese, garlic salt and basil.
Once breadsticks are removed from oven, brush generously with butter parmesan mixture and serve.