In a stand mixer bowl, combine the warm water, sugar, and yeast and mix well. Let it sit for about 5 minutes, or until it becomes frothy and bubbly.
Once your yeast has proofed, add the avocado oil, salt, and about 1½ cups of flour. Using a dough hook, mix until all the ingredients are completely combined. Add up to 2 more cups of flour, about a 1/4 cup at a time, just until the dough pulls away from the edges of the bowl.
Mix on low speed for another 1-2 minutes, then cover and let the dough rest in a warm place for 30-45 minutes, or until about doubled in size.
Preheat the oven to 375 degrees F.
Lightly grease your hands, then gently pull the dough out of the bowl and place on the counter. Divide the dough into 2 pieces and use a rolling pin to roll the dough to roughly 12" by 18" pieces, then place into a lightly greased baking sheet. Gently pull and press the dough until it covers the bottom, then continue to roll the second half of the dough the same as the first.
In a small bowl, combine the melted butter, brown sugar, and cinnamon powder. Mix, then use the back of a spoon to spread the cinnamon mixture onto the dough in the baking sheet.
Place the second sheet of dough onto the first. Pull the dough gently to match up the edges of the dough. Use a pizza cutter to cut the dough in half and then into 1½" strips. Gently twist each of the strips about 2-3 times, then let them rest for about 15 minutes.
Once they have had a chance to rest, bake in your preheated oven for 18-20 minutes, or until the bottom and the top are golden brown.
While they are baking, beat the room temperature butter in a stand mixer until light and fluffy. Turn the mixer down very low and add the powdered sugar, 2 tablespoons of milk, and the vanilla. Mix on low until all the ingredients are combined, add more milk or powdered sugar as needed. Mix until smooth.
Remove the breadsticks from the oven once baked and drizzle the icing over the top. Enjoy!