In a small bowl, stir together the warm water, 1 tablespoon of sugar and yeast until it dissolves. Let the mixture stand for a few minutes or until you see bubbles resembling foam. This is the way of proofing yeast to make sure it is “alive”. If the mixture doesn’t foam, then you need to start over.
In a small saucepan over low heat, melt 6 tablespoons of butter. Stir in the milk and heat the mixture until lukewarm, about 110 to 115 degrees F. You can use the microwave, if you prefer.
Pour the butter and milk mixture into a large bowl. Add the yeast mixture and the remaining 2 tablespoons of sugar. Add the bread flour and salt and using a wooden spoon, mix until just combined. Stir in the ¾ cups of all-purpose flour and mix until just incorporated.
Dump the dough onto a clean work surface and begin to bring the dough together into a ball. If the dough is too sticky, add more all-purpose flour in small increments (use up to ½ cup of additional a/p flour). The dough should be slightly sticky, yet easy to handle.
Knead the dough for about 8-10 minutes, adding extra flour if needed until the dough is smooth, elastic yet a bit sticky.
Form the dough into a ball and place it in a large bowl greased with butter. Cover with plastic wrap or a towel and let the dough rest in a draft free place, for about an hour or until doubled in size.
Butter a 9×13-inch baking pan. Divide the dough into 20 equal pieces. Roll each one into a ball and arrange evenly in 4 rows of 5 in the baking pan. Cover loosely with plastic wrap and let rise in a warm, draft free place until almost doubled in size, about 45 minutes.
Using a floured chopstick or the edge of a ruler, make a deep crease down the center of each row of rolls. Let rolls rise, loosely covered for 15 minutes.
Preheat oven to 375 degrees F and place a rack in the center of the oven.
Melt the remaining 2 tablespoons of butter and cool slightly. Brush the tops of the rolls with butter and place in the oven for 20-25 minutes, until golden brown. Cool rolls in the pan for 5 minutes then remove and serve warm.