For dough: In a medium bowl, whisk together warm milk, 1 tablespoon (12 grams) granulated sugar, and yeast. Let stand until foamy, about 10 minutes.
In the bowl of a stand mixer, whisk together 1 cup (125 grams) flour, salt, and remaining 3 tablespoons (36 grams) granulated sugar by hand. Add yeast mixture and eggs. Using the paddle attachment, beat at medium-low speed until mostly smooth, 2 to 3 minutes, stopping to scrape sides of bowl. Add 1 cup (125 grams) flour; beat at low speed just until combined and a shaggy dough forms.
Switch to the dough hook attachment. Beat at medium-low speed until dough is soft, elastic, and smooth, sticks to bottom of bowl (but isn’t overly sticky), and gathers around dough hook, 6 to 8 minutes, stopping to scrape sides of bowl; add up to remaining ¼ cup (31 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. Add butter, 1 tablespoon (14 grams) at a time, beating until combined after each addition. Beat until dough is smooth and elastic, pulls away from bottom and sides of bowl, and passes the windowpane test (see page 66), 6 to 8 minutes.
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, about 1 hour.
Punch down dough, and turn out onto a lightly floured surface. Flatten into a rectangle, and transfer to a parchment paper-lined baking sheet. Cover and refrigerate for at least 5 hours or up to overnight.
Line rimmed baking sheets with parchment paper.
Divide dough into 10 portions (about 60 grams each). Shape into rounds, and place at least 3 inches apart on prepared pans. Cover and let rest for 10 minutes.
Flatten dough portions into 2½-inch rounds. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed, 45 minutes to 1 hour.
For filling: In another medium bowl, whisk together cream cheese and granulated sugar until smooth. Add egg yolks and vanilla, and whisk until smooth and no lumps remain. Spoon filling into a pastry bag, and cut a ½-inch opening in tip.
Preheat oven to 375°F (190°C).
In a small bowl, whisk together egg and 1 tablespoon (15 grams) water.
Using your fingers, gently press down center of each round, creating a 2½-inch indentation. (Each bun should be about 3½ inches wide now.) Brush with egg wash. Pipe filling into center of each bun (about 2 tablespoons or 30 grams each). Top each with 1 teaspoon (4 grams) pumpkin butter; swirl together with a wooden pick.
Bake until golden brown and an instant-read thermometer inserted in center of bread registers at least 190°F (88°C), 10 to 12 minutes, rotating pans halfway through baking. Let cool on pans for 10 minutes. Remove from pans, and let cool completely on a wire rack. Just before serving, garnish with confectioners’ sugar, if desired. Refrigerate in an airtight container for up to 3 days.
