Step 1: In a large bowl, combine the warm milk, yeast, and 1 tablespoon of the granulated sugar. Stir gently and let it sit for 5-10 minutes until foamy. This indicates the yeast is active.
Step 2: Add the remaining sugar, salt, melted butter, and egg to the yeast mixture. Whisk until well combined.
Step 3: Gradually add 3 cups of flour, one cup at a time, mixing with a wooden spoon until a shaggy dough forms. Add more flour, about 1/4 cup at a time, until the dough comes together and is no longer sticky, but still soft. You might not need all 4 cups.
Step 4: Turn the dough out onto a lightly floured surface and knead for 8-10 minutes until it is smooth and elastic. The dough should spring back when lightly poked.
Step 5: Lightly grease a large bowl with oil. Place the dough in the bowl, turning once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 to 1.5 hours, or until doubled in size.
Step 6: Once doubled, gently punch down the dough to release the air. Turn the dough out onto a lightly floured surface and divide it into 12-15 equal pieces. Shape each piece into a smooth ball.
Step 7: Arrange the shaped rolls in a lightly greased 9x13 inch baking dish, leaving a little space between each roll. Cover the dish again and let the rolls rise for a second time in a warm place for another 30-45 minutes, or until puffy and almost doubled.
Step 8: Preheat your oven to 375°F (190°C) during the last 15 minutes of the second rise.
Step 9: Bake the rolls for 15-20 minutes, or until golden brown on top. If they start browning too quickly, you can loosely tent them with foil.
Step 10: Once out of the oven, immediately brush the tops of the hot rolls with the 2 tablespoons of melted butter. Serve warm and enjoy!