Instructions

• Fit a stand mixer with the paddle attachment. Add 2 cups (250 grams) of the all-purpose flour, granulated sugar (¼ cup / 50 g), kosher salt (4¼ teaspoons / 12.75 g), and the instant yeast (7 g). Beat at medium-low speed just until combined.
• Measure out the water called for in the ingredient list (1? cups (320 grams) plus 1 tablespoon (15 grams), divided). Reserve the 1 tablespoon (15 g) for the egg wash. In a medium saucepan, combine the remaining 1? cups (320 g) water, whole milk (½ cup / 120 g), olive oil (¼ cup / 56 g), and the softened unsalted butter (2 tablespoons / 28 g). Cook over medium heat, stirring frequently, until the butter is melted and an instant-read thermometer reads 120°F to 130°F (49°C to 54°C). Remove from heat.
• With the mixer running at medium-low, pour the warm milk mixture into the flour mixture. Beat about 1 minute until combined, stopping once to scrape the sides of the bowl.
• With the mixer on low speed, gradually add 3½ cups (438 grams) of the all-purpose flour, beating just until combined.
• Replace the paddle with the dough hook. Beat at medium-low speed for 4 to 6 minutes, stopping occasionally to scrape the bowl and dough hook, until a soft, slightly sticky dough forms. If the dough is too sticky to handle, add up to the remaining ¼ cup (31 grams) flour, 1 tablespoon (8 grams) at a time, until the dough is soft and passes the windowpane test (it may still stick slightly to the sides of the bowl).
• Lightly spray a large bowl with cooking spray. Transfer the dough to the bowl and turn to grease the top. Cover and let the dough rise in a warm, draft-free place (about 75°F / 24°C) until doubled in size, about 40 minutes to 1 hour.
• Position an oven rack in the top third of the oven and preheat the oven to 425°F (220°C). Line 3 rimmed baking sheets with parchment paper.
• Punch down the dough and cover it; let it rest for 10 minutes. On a lightly floured clean surface, divide the dough into 24 equal portions (about 51 grams each). Keep the portions covered with plastic wrap while you work.
• Shape each portion into a ball, then cover and let the balls rest 10 minutes. After resting, gently flatten each ball to release large air bubbles and shape each into an even 9- to 10-inch rope (very lightly flour your surface or hands if needed). Place each rope seam side down on the prepared pans, spacing them about 1 inch apart. (The ropes will shrink to about 7 to 8 inches; press in any pointed ends to round the ropes if needed.)
• Cover the pans and let the shaped breadsticks rise in a warm, draft-free place (about 75°F / 24°C) until puffed and the dough holds an indentation when poked, about 25 to 35 minutes.
• In a small bowl, whisk together the lightly beaten large egg (50 g) and the reserved 1 tablespoon (15 g) water. Brush the egg wash evenly over the risen dough.
• Bake one pan at a time on the top-third rack until the breadsticks are golden brown, 10 to 12 minutes. Remove the pan from the oven and let the breadsticks cool on the pan for 5 minutes.
• In a small bowl, stir together the melted unsalted butter (¼ cup / 57 g), garlic salt (½ teaspoon / 3 g), and dried Italian seasoning (½ teaspoon). Brush the warm breadsticks with this butter mixture. Garnish with grated fresh Parmesan cheese if desired and serve warm.