In a small bowl, combine tangzhong ingredients and stir until it turns into a shaggy ball of dough. Set aside.
In a mixing bowl, dissolve yeast in warm water. Add about a teaspoon of the sugar and let the mixture sit for about 5 minutes, or until foamy. Add the remaining sugar, eggs, salt, melted butter, and the tangzhong. Stir everything well with a wooden spoon.
Add the flour gradually, continuing to mix until a soft and shaggy ball of dough forms. Turn the dough over on lightly floured board and knead the dough until it is smooth and elastic. Dust sparingly with more flour when the dough is sticking too much. Shape the dough into a ball and place it inside a bowl. Cover it with a kitchen towel and let the dough rise for 1 to 1 and 1/2 hours. The dough should be doubled in size.
Gently deflate the risen dough and pat it into a disc. Using a rolling pin, roll the dough into a circle that is 16 inches in diameter. Using a pizza cutter, slice the circular dough into 12 triangles.
Roll each triangle starting from the wide edge down to the narrow edge. Arrange the rolls in a large baking sheet that is lined with parchment paper. Cover once more with a kitchen towel and let rise again for 1 hour or until the rolls are puffy.
Preheat oven to 350 F. Lightly beat together the egg wash ingredients and brush the rolls with it. Bake the salted butter rolls for 18-21 minutes. Brush with melted salted butter. Sprinkle with a pinch of salt.