In the bowl of a stand mixer (see Notes) fitted with the paddle attachment, beat ½ cup (63 grams) flour, sugar, ¾ teaspoon (2.25 grams) salt, yeast, and ¼ teaspoon onion powder at low speed until combined.

In a small microwave-safe bowl, combine 3 tablespoons (45 grams) water, milk, and 1 tablespoon (14 grams) butter; heat on high in 10-second intervals, stirring between each, 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 ½ cup (63 grams) flour and chopped sage, beating just until combined.

Turn out dough onto a very lightly floured surface, and knead by hand until dough passes the windowpane test (see Notes), 10 to 16 minutes; add up to remaining ¼ cup (31 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too wet or sticky. (Dough should be soft and somewhat sticky; re-flour surface only if needed.)

Spray a medium 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 saucepan, heat remaining 4 tablespoons (56 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.) Discard sage leaves. Stir in remaining ¼ teaspoon salt and remaining ¼ teaspoon onion powder.

Spray a 4- to 5-cup Bundtlette pan with baking spray with flour.

Punch down dough; let stand for 10 minutes. On a clean surface, divide dough into 54 portions (about 4 grams each). Roll each portion into a smooth ball, pinching any seams to seal. (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 9 dough balls, side by side, in an even layer in each well. Pour any remaining butter mixture over top of dough and firmly press balls in an even layer in wells. 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.

Preheat oven to 350°F (180°C).

Bake until tops are lightly golden, and an instant-read thermometer inserted near center registers 195°F (90°C) to 210°F (98°C), 10 to 14 minutes. Let cool in pan for 5 minutes; invert onto a serving plate. Garnish with cheese, if desired. Serve immediately.