In the bowl of a stand mixer fitted with the paddle attachment, combine 1¼ cups (156 grams) flour, sugar, 2¼ teaspoons (6.75 grams) salt, yeast, and nutmeg; beat at low speed until combined.

In a medium saucepan, cook milk and softened butter over medium heat 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 speed for 2 minutes, stopping to scrape sides of bowl. Add egg; beat at medium-high speed for 2 minutes. With mixer on low speed, gradually add 2 cups (250 grams) flour, beating until combined.

Switch to the dough hook attachment. Beat at medium-low speed until a soft, somewhat tacky dough forms, 6 to 8 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, if dough is too sticky. (Dough should pass the windowpane test; see Note.)

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.

In a small bowl, stir together melted butter, chives, tarragon, parsley, garlic powder, red pepper, and remaining ¼ teaspoon salt.

Preheat oven to 350°F (180°C).

Punch down dough; let stand for 5 minutes. On a clean surface, divide dough into 36 portions (about 24 grams each); gently shape each portion into a ball, pinching closed any seams if needed. (Keep dough portions covered with a sheet of plastic wrap while working.)

Spray a 15-cup Nordic Ware Anniversary Bundt Pan with baking spray with flour.

Dip dough balls in butter mixture, turning until well coated; arrange evenly in prepared pan, pressing dough balls gently into each other and grooves of pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size and dough holds an indentation when pressed, 25 to 35 minutes. Reserve remaining butter mixture.

Bake until golden brown and an instant-read thermometer inserted near center registers at least 190°F (88°C), 25 to 30 minutes. Let cool in pan for 5 minutes; invert onto a serving plate.

Reheat reserved butter mixture, if necessary; brush all over warm bread. Sprinkle with Parmesan; serve immediately.