Within the bowl of a stand mixer, whisk collectively 1 cup (125 grams) flour, sugar, salt, yeast, and baking soda by hand.
In a small saucepan, warmth 3⁄4 cup(180 grams) water and three tablespoons (42 grams) butter over medium-low warmth till butter is melted and an instant-read thermometer registers 120°F (49°C) to130°F (54°C). Add heat butter combination and ricotta to flour combination; utilizing the paddle attachment, beat at medium-low velocity till mixed, about 1 minute, stopping to scrape sides of bowl. With mixer on low velocity, step by step add 2 1⁄4 cups (281 grams) flour, beating simply till mixed and stopping to scrape sides of bowl.
Change to the dough hook attachment. Beat at medium-low velocity till a delicate, considerably sticky dough types, 12 to fifteen minutes, stopping to scrape sides of bowl and dough hook; add as much as remaining 1⁄4 cup (31 grams) flour, 1 tablespoon (8 grams) at a time, if dough is just too sticky. (Dough will principally draw back from sides of bowl.) Prove dough onto a calmly floured floor, and form right into a ball.
Spray a big bowl with cooking spray. Place dough in bowl, turning to grease high. Cowl and let rise in a heat, draft-free place (75°F/24°C) till doubled in dimension, 30 to 45 minutes.
Punch down dough; cowl and let stand for 10 minutes.
In a small microwave-safe bowl, warmth remaining 5 tablespoons (71 grams) butter on excessive in 10-second intervals till melted. In one other small bowl, stir collectively provolone and Parmesan.
Spray a 12-cup muffin pan with baking spray with flour.
On a calmly floured floor, divide dough in half. Roll half of dough right into a 12-inch sq.. (Preserve remaining dough coated with plastic wrap.) Brush 1 tablespoon (14 grams) melted butter onto dough. Reduce dough into 12 (6×2-inch) strips. Sprinkle 1 tablespoon (8 grams) cheese combination onto every of 10 strips. Stack 5 strips, cheese aspect up, on high of one another; place 1 plain strip, butter aspect down, on high. Repeat with remaining 6 strips of dough. Utilizing a floured serrated knife, lower every dough stack crosswise into 3 (2-inch) squares. Place dough squares, lower aspect up, in ready muffin cups. Repeat process with remaining dough, 1 tablespoon (14 grams) melted butter, and cheese combination. Sprinkle any remaining cheese combination onto dough in cups. Loosely cowl dough with plastic wrap, and let rise in a heat, draft-free place (75°F/24°C) till dough fills cups, 15 to 25 minutes.
Preheat oven to 375°F (190°C).
In a small bowl, whisk collectively egg and remaining 1 tablespoon (15 grams) water; brush onto dough.
Bake till calmly browned,12 to fifteen minutes. Let cool in pan on a wire rack for 10 minutes. Stir parsley into remaining melted butter; brush onto rolls. Serve heat.