Garlic Breadsticks

In the bowl of a stand mixer fitted with the paddle attachment, beat 2 cups (250 grams) flour, sugar, salt, and yeast at medium-low speed just until combined.

In a medium saucepan, combine 1⅓ cups (320 grams) water, milk, oil, and softened butter; cook over medium heat, stirring frequently, until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm milk mixture to flour mixture; beat at medium-low speed until combined, about 1 minute, stopping to scrape sides of bowl. With mixer on low speed, gradually add 3½ cups (438 grams) flour, beating just until combined.

Switch to the dough hook attachment. Beat at medium-low speed until a soft, slightly sticky dough forms, 4 to 6 minutes, stopping to scrape sides of bowl and dough hook; add up to remaining ¼ cup (31 grams) flour, 1 tablespoon (8 grams) at a time, as needed if dough is too sticky. (Dough should pass the windowpane test [see Note] but may still stick slightly to sides of bowl.)

Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 40 minutes to 1 hour.

Position oven rack in top third of oven. Preheat oven to 425°F (220°C). Line 3 rimmed baking sheets with parchment paper.

Punch down dough; cover and let stand for 10 minutes. On a clean surface, divide dough into 24 portions (about 51 grams each), and cover with a sheet of plastic wrap. Shape each portion into a ball; cover and let stand for 10 minutes. Gently flatten each ball to release large air bubbles; shape each portion into an even 9- to 10-inch rope, very lightly flouring surface or hands as needed. Place, seam side down, 1 inch apart on prepared pans. (Dough ropes will shrink to 7 to 8 inches.) Press in any pointed ends to make dough ropes more rounded, if necessary. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed and dough holds an indentation when poked, 25 to 35 minutes.

In a small bowl, whisk together egg and remaining 1 tablespoon (15 grams) water. Brush egg wash onto dough.

Bake, one batch at a time, until golden brown, 10 to 12 minutes. Let cool on pan for 5 minutes.

In a small bowl, stir together melted butter, garlic salt, and Italian seasoning. Brush warm breadsticks with butter mixture. Garnish with Parmesan, if desired. Serve warm.