In a mixing bowl, combine warm water, yeast, and sugar. Allow it to sit for about 5 minutes until it becomes frothy.
Add flour, salt, and olive oil to the yeast mixture. Stir until a dough forms.
Knead the dough on a floured surface for about 5 minutes until smooth and elastic.
Place the dough in a greased bowl, cover it with a clean cloth, and let it rise in a warm area for about 30 minutes, until doubled in size.
Preheat the oven to 425°F (220°C) and line a baking sheet with parchment paper.
After the dough has risen, punch it down and roll it out on a floured surface into a rectangle, about ½ inch thick.
Sprinkle the shredded mozzarella evenly over the dough and use a rolling pin to gently press the cheese into the dough.
Cut the dough into strips using a pizza cutter or knife to form sticks.
Place the breadsticks on the prepared baking sheet, spacing them about an inch apart.
In a small bowl, mix melted butter, garlic powder, and oregano. Brush this mixture over the tops of the breadsticks.
Bake in the preheated oven for 15 minutes, or until golden and bubbly.
Remove from the oven and let them cool slightly before serving. Serve warm with marinara sauce for dipping, if desired.