In the bowl of a stand mixer fitted with the paddle attachment, stir together 4 cups (500g) flour, granulated sugar, yeast, and salt by hand.
In a small saucepan, heat 1 cup (240g) water and 1/2 cup (113g) melted butter over medium heat until an instant-read thermometer registers 120°F (49°C) to 130°F (54°F). Add water mixture to flour mixture, and beat at medium speed for 2 minutes. Add 1 egg (50g) and egg yolk, and beat for 2 minutes. Beat in enough of remaining 1/2 cup (63g) flour until a soft dough forms. (Dough will be sticky.)
Switch to the dough hook attachment. Beat at low speed until dough is smooth and elastic, 6 to 8 minutes.
Lightly oil a large bowl. Shape dough into a smooth ball, and place 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 45 minutes.
Butter a 12-cup muffin pan.
In a small bowl, stir together peanut butter, confectioners’ sugar, vanilla, and remaining 1 tablespoon (14g) melted butter.
Lightly punch down dough. On a lightly floured surface, roll dough into a 20x12-inch rectangle. Spread peanut butter mixture onto dough. Sprinkle with chocolate. Fold rectangle crosswise into thirds, forming a smaller rectangle, about 12x6½ inches.
Cut rectangle crosswise into 12 (about 1 inch) strips. Gently stretch and twist each strip; coil one strip into each prepared muffin cup, tucking end inside edge of cup to create a rounded top. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed, about 30 minutes.
Preheat oven to 325°F (170°C).
In a small bowl, whisk together remaining 1 egg (50g) and remaining 1 tablespoon (15g) water. Brush tops of dough with egg wash.
Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 15 to 20 minutes. Serve warm.