1. Combine water, sugar, and yeast in the bowl of a stand mixer fitted with a hook; let sit until foamy, about 10 minutes. Add 9 tbsp. butter, plus dry milk, shortening, salt, and herbs; mix until combined. With the motor running, slowly add flour until dough comes together. Increase speed to medium-high; knead dough until smooth, 1–2 minutes. Cover loosely with plastic wrap; set in a warm place until doubled in size, about 1 hour.
2. On a lightly floured surface, roll dough into a 6" × 13" rectangle about ½" thick. Spread remaining butter over dough, leaving a ½" border. Fold dough in thirds as you would a letter. Rotate dough 90°; roll dough into a 6" × 13" rectangle and fold in thirds again. Rotate, roll, and fold dough twice more. Transfer to a lightly floured baking sheet and cover with plastic wrap; chill overnight.
3. Next day, cut dough into twelve 2" squares and place cut side up in an ungreased muffin tin. Cover loosely with plastic wrap; set in a warm place until doubled in size, about 45 minutes.
4. Heat oven to 375°. Bake rolls, rotating once halfway through, until golden brown and cooked through, about 30 minutes. Let cool slightly before serving.