1. Prepare the Tangzhong: In a small saucepan, whisk together 1/4 cup of the water and 2 tablespoons of all-purpose flour until smooth. Cook over medium-low heat, stirring constantly, until the mixture thickens into a paste, about 2-3 minutes. It should resemble a thick gravy. Remove from heat and let it cool completely. This step is crucial for the rolls’ incredible softness.

2. Combine Wet Ingredients: In a large mixing bowl, combine the cooled tangzhong, active sourdough starter, the remaining 1/4 cup of water, granulated sugar, salt, egg, and 1/4 cup of melted and cooled butter. Whisk everything together until well combined and smooth.

3. Add Flour and Mix Dough: Gradually add the 3 cups of all-purpose flour to the wet ingredients, mixing with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms. Once the flour is mostly incorporated, turn the dough out onto a lightly floured surface.

4. Knead the Dough: Knead the dough for about 8-10 minutes until it becomes smooth, elastic, and no longer sticky. If using a stand mixer, knead on medium speed for 6-8 minutes. The dough should spring back when lightly poked. This develops the gluten, which is key for a soft, chewy texture.

5. First Rest and Shape: Place the kneaded dough in a lightly oiled bowl, turning it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rest in a warm place for 30-45 minutes, or until slightly puffy. After resting, gently punch down the dough and divide it into 12 equal pieces. Shape each piece into a smooth ball.

6. Second Rise and Preheat Oven: Arrange the shaped dough balls in a lightly greased 9×13 inch baking dish, leaving a little space between each roll. Cover the dish and let the rolls rise in a warm place for another 20-30 minutes, or until they look visibly puffy and almost doubled in size. Towards the end of this rise, preheat your oven to 375 F (190 C).

7. Bake the Rolls: Bake the rolls in the preheated oven for 20-25 minutes, or until they are golden brown on top and cooked through. The internal temperature should reach around 200-210 F (93-99 C).

8. Finish with Butter: As soon as the rolls come out of the oven, brush the tops with the remaining 1 tablespoon of melted butter. This adds a beautiful sheen and extra flavor. Serve warm and enjoy!