Chocolate-Cherry Brioche Buns

In the bowl of a stand mixer, whisk together 1⅔ cups (208 grams) flour, sugar, yeast, and salt. Add warm milk, 2 eggs (100 grams), and Tangzhong; using the paddle attachment, beat at low speed until combined, about 1 minute. With mixer on low speed, gradually add remaining 1 cup (125 grams) flour, beating until a shaggy dough forms; scrape sides of bowl.

Switch to the dough hook attachment. Beat at medium-low speed until dough becomes smooth, elastic, and slightly tacky, 8 to 11 minutes. (Dough should pull away from sides of bowl.) With mixer on medium-low speed, add butter, 1 tablespoon (14 grams) at a time, beating until combined after each addition (7 to 8 minutes total). Increase mixer speed to medium, and beat until a smooth, elastic dough forms, about 10 minutes. Reduce mixer speed to low; add chocolate and cherries, beating until well combined.

Lightly oil a large bowl. 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, 1 to 1½ hours.

Line baking sheets with parchment paper.

Turn out dough onto a clean surface, and punch down dough. Press dough into a 10×8-inch rectangle. Divide dough into 20 portions (about 45 grams each). Using your hands, gently roll each portion into a smooth ball, lightly flouring your hands as needed. Place 3 to 4 inches apart on prepared pans. Cover with lightly greased plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, about 1 hour.

Preheat oven to 375°F (190°C).

In a small bowl, whisk together 1 tablespoon (15 grams) water and remaining 1 egg (50 grams); brushonto dough.

Bake until golden brown and an instant-read thermometer inserted near center registers 190°F (88°C), 8 to 10 minutes. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on a wire rack. Store in an airtight container for up to 3 days.

In a small saucepan, whisk together milk and flour; cook over medium-low heat, whisking constantly, until thickened, whisk leaves lines on bottom of pan, and an instant-read thermometer registers 150°F (66°C). (Mixture will look like mashed potatoes.) Transfer to a small bowl, and let cool until an instant-read thermometer registers 130°F (54°C) or until room temperature.