2 ¼ teaspoons active dry yeast (about half a packet)
3 tablespoons sugar
3 ¾ cups all-purpose flour, plus more if needed
¼ cup olive oil
2 teaspoons fine sea salt
For the Topping:
4 tablespoons unsalted butter
1 ½ teaspoons dried parsley
1 teaspoon fine sea salt
1 teaspoon garlic powder (or use 2 teaspoons garlic salt in place of salt and garlic powder)
¼ cup finely grated Parmigiano Reggiano cheese
Whisk ¼ cup warm water with the yeast and ½ teaspoon of the sugar in a small bowl and let sit for 10 minutes; it should be frothy and bubbly (this is called “bloomed” yeast). If not, your yeast is dead—throw it out and start over.
Combine the yeast mixture with the remaining water, flour, olive oil, salt, and the remaining 2 ½ tablespoons sugar in the bowl of a stand mixer fitted with the dough hook attachment. Mix on medium speed until the dough is slightly tacky and elastic and pulls away from the sides of the bowl (add flour by the tablespoonful if too wet and water by the tablespoonful if too dry), stopping the mixer to scrape down the sides occasionally so everything is well mixed (about 8 minutes total). Transfer the dough to a lightly oiled bowl, cover with plastic wrap, and let rise in a warm place until doubled in size, 2 hours.
Uncover the dough, punch it down, and move it from the bowl to a lightly floured work surface. Divide the dough into 10 equal-sized balls (use a kitchen scale if you have one! If you don’t then just eyeball it). Cover the dough balls with a damp kitchen towel. One at a time, use oiled hands to form each ball into an 8-x-1-inch baton and arrange on two lightly oiled baking sheets, making sure to leave at least an inch between breadsticks so they don’t stick together during the second rise. Cover loosely with plastic wrap or a clean plastic bag and let rise again until the breadsticks increase in size by about 50 percent, about 1 hour.
When the breadsticks have about 30 minutes left of their second rise, preheat the oven to 400°F; after the full hour, once the breadsticks have risen again, if they’ve widened considerably elongate them again with lightly oiled hands if necessary.
Bake the breadsticks until lightly browned with smooth tops, rotating the pan halfway through, 11 to 12 minutes total.
While the breadsticks are baking, combine the butter, parsley, salt, and garlic powder in a microwave-safe bowl and heat for 30 seconds until butter is melted. Remove the breadsticks from the oven; brush on the herb butter, sprinkle with Parm, and serve immediately.