In a small bowl, combine warm milk, 1 tablespoon (12 grams) sugar, and yeast. Let stand until foamy, 5 to 10 minutes.
In the bowl of a stand mixer, whisk together flour, dry milk, salt, and xanthan gum, and remaining 3 tablespoons (36 grams) sugar by hand until combined. Using the paddle attachment, with mixer on low speed, add melted butter, 2 eggs (100 grams), and yeast mixture, beating just until combined, stopping to scrape bottom and sides of bowl. Increase mixer speed to medium-high, and beat for 10 minutes, stopping to scrape sides and bottom of bowl and paddle. (Dough will look like a thick muffin batter.) Scrape sides and bottom of bowl and paddle. Cover and let stand in a warm, draft-free place (75°F/24°C) until puffed, about 1 hour.
Using a spatula, lightly knead and deflate dough. Cover and refrigerate dough for 2 hours.
Spray an 8-inch square baking pan with cooking spray.
Lightly spray a work surface with cooking spray or coat with vegetable oil. Turn out dough onto work surface, and divide into 9 portions (about 110 grams each). (Dough will be very soft and pliable.) Using your hand, roll each portion on greased surface into a smooth ball. Place in prepared pan. (If dough becomes too soft or sticky to work with, refrigerate for 5 to 10 minutes to firm up, greasing work surface again if needed.) Cover and let rise in a warm, draft- free place (75°F/24°C) until puffed and sides of rolls are touching, about 45 minutes.
Preheat oven to 350°F (180°C).
In a small bowl, whisk together 1 tablespoon (15 grams) water and remaining 1 egg (50 grams); brush egg wash onto rolls.
Bake until golden brown and an instant- read thermometer inserted in center registers 190°F (88°C), about 35 minutes, loosely covering with foil during final 10 minutes of baking to prevent excess browning. Let cool in pan on a wire rack for 10 minutes.
In a small microwave-safe bowl, combine cubed butter, thyme, parsley, and garlic. Heat on high in 15-second intervals until butter is melted. Brush butter mixture onto warm rolls. Serve warm.