Breadsticks with Parmesan Butter

1 cup warm water (110 degrees F/45 degrees C)

1 tablespoon white sugar

2 (.25 ounce) packages active dry yeast

3 tablespoons vegetable oil

1 egg

1 teaspoon salt

2 cups all-purpose flour

7 tablespoons white sugar

1 cup warm water (110 degrees F/45 degrees C)

2 ½ cups all-purpose flour, or as needed

½ cup butter, softened

2 tablespoons grated Parmesan cheese

¼ teaspoon garlic powder

Mix 1 cup warm water, 1 tablespoon sugar, and yeast together in a large bowl; let stand until yeast softens and begins to form a creamy foam, about 5 minutes. Add vegetable oil, egg, salt, 2 cups flour, 7 tablespoons sugar, and 1 cup warm water; beat with an electric mixer until smooth. Stir in remaining 2 1/2 cups flour until dough is soft.

Turn dough onto a floured surface; knead until smooth and elastic, 6 to 8 minutes. Place in a greased bowl, turning once to grease the top of dough. Cover and let rise in a warm place until doubled in size, about 40 minutes.

Preheat oven to 400 degrees F (200 degrees C). Grease 2 to 3 baking sheets.

Punch dough down and turn onto a floured surface. Divide dough into 36 pieces. Shape each piece into a 6-inch rope. Arrange on the prepared baking sheet, 2 inches apart. Cover and let rise until doubled in size, about 25 minutes.

Bake in the preheated oven until golden brown, 10 to 12 minutes.

Beat butter, Parmesan cheese, and garlic powder together in a bowl until creamy; serve alongside baked breadsticks.