Knead together yogurt, egg, 1/2 tsp garlic powder, and 1 cup + 1 tbsp flour (reserve extra tbsp for flouring your hands and dough when it gets too sticky).
Roll out dough into a log shape, then cut into 8 pieces. Roll each piece into a breadstick shape (about 8 inches long). Arrange on a cookie sheet sprayed with oil.
Cover dough with a kitchen towel and let rise for about 5 minutes. They'll rise even more in the oven.
Bake at 400 for 10 minutes. Meanwhile, microwave butter, oregano, and remaining 1/2 tsp garlic powder until melted.
Remove breadsticks from oven and brush with 1/2 the butter mixture. Sprinkle with parmesan and bake for another 5 minutes. Remove from oven and brush with remaining butter mixture.