In the bowl of a stand mixer fitted with the paddle attachment, beat 1 cup (125 grams) flour, sugar, 2¾ teaspoons (8.25 grams) salt, yeast, and ½ teaspoon (1 gram) onion powder at low speed until combined.

In a small saucepan, heat ½ cup (120 grams) water, milk, and 2 tablespoons (28 grams) butter over medium heat, stirring occasionally, 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 1 minute, stopping to scrape sides of bowl. Add squash; beat just until combined, about 30 seconds. With mixer on low speed, gradually add 2 cups (250 grams) flour and chopped sage, beating just until combined.

Switch to the dough hook attachment. Beat at low speed until dough is soft and somewhat sticky and mostly clears sides of bowl, 8 to 12 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 Notes.) Turn out onto a lightly floured surface, and shape into a ball.

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, 50 minutes to 1 hour.

Preheat oven to 350°F (180°C).

In a small saucepan, heat remaining 6 tablespoons (84 grams) butter over medium heat until bubbling. Add sage leaves; cook, stirring occasionally, until leaves are slightly crisp and butter solids are light amber in color and nutty in aroma, 3 to 6 minutes. Transfer butter mixture to a small heatproof bowl; let cool for 15 minutes. (Butter should be just warm to the touch.) Remove and discard sage. Stir in remaining ¾ teaspoon (2.25 grams) salt and remaining ½ teaspoon (1 gram) onion powder.

Spray a 12-cup Bundt pan with baking spray with flour.

Punch down dough; let stand for 10 minutes. On a clean surface, divide dough into 30 portions (26 to 28 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.) Dip dough balls in butter mixture, turning until well coated and letting excess drip off; arrange evenly in prepared pan, firmly pressing dough balls into each other and grooves of pan. Pour and spread remaining butter mixture over top of dough; firmly press dough balls in an even layer in pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed and dough holds an indentation when pressed, 25 to 35 minutes.

Bake until top of dough starts to turn golden brown and an instant-read thermometer inserted near center registers at least 195°F (88°C) to 210°F (98°C), 17 to 22 minutes. Let cool in pan for 5 minutes; invert onto a serving plate. Garnish with cheese, if desired. Serve immediately.