In a large bowl or the bowl of a stand mixer, dissolve the yeast and sugar in the warm water. Let sit until foamy and bubbly, which indicates that the yeast is active.
Add the salt, oil, and two cups of flour to the yeast mixture, then mix until combined. Gradually add more flour, ¼ cup at a time, until you achieve a soft dough that pulls away from the sides of the bowl.
Knead the dough until it becomes smooth and elastic. Once ready, place it in a greased bowl, cover it with plastic wrap or a clean kitchen towel, and let rise in a warm area for about one hour.
After rising, gently punch down the dough to release air bubbles and divide it into 16 equal pieces. Roll each piece into a 12-inch rope, then create slits on either side to form bone shapes by twisting both ends in opposite directions.
Place shaped breadsticks onto a greased or parchment-lined baking sheet and cover them again. Allow them to rise for another 45 minutes to an hour until they have doubled in size.
Preheat your oven to 425℉ during the last few minutes of rising time. Bake your breadsticks for about 12-14 minutes until they are golden brown, then brush with melted butter and sprinkle with garlic salt and parmesan before serving warm with marinara sauce on the side.