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Step 1
Pour the milk into the bowl of a standing mixer, and add the sugar and yeast. Stir to combine and then let sit for about 5 minutes to let the yeast begin to come alive. (*See note) Whisk in the egg, egg yolk and 6 tablespoons melted butter.
Step 2
Fit your mixer with the dough hook, add 5 cups of the flour and mix on low speed until the dough begins to come together. Slowly add enough of the remaining cup of flour so that the dough forms a soft, slightly sticky ball. This might take the entire remaining cup or only a bit of it. What you're looking for is a soft, smooth ball of dough that clings to the dough hook, does not stick to the sides of the bowl, but does stick slightly to the bottom of the bowl.
Step 3
Once the dough has come together, sprinkle in the salt. Continue to knead the dough for about 8-10 minutes. At this point, the dough should be very soft and smooth.
Step 4
Brush the inside of a large bowl with a thin layer of the melted salted butter and dump the dough into the bowl. Brush the top of the dough with a bit of the melted salted butter and cover with plastic wrap. Let the dough rise at room temperature for 1-2 hours, until it's doubled in size. The warmer the room, the faster the dough will rise. (*See the tips earlier in the post about speeding up and slowing down the dough's rise time.)
Step 5
After the dough has risen, dump it out of the bowl onto a clean work surface. Using a dough knife or large butcher knife, cut the dough in half. Then cut each half into 12 equal pieces.
Step 6
Brush the inside of two 9x13 baking dishes with some of the melted salted butter.
Step 7
Shape each piece of dough into a ball by gently stretching the outside of each piece into an oblong, pinching the sides together at the bottom. Bring the opposite sides together and pinch together at the bottom. (*See the video earlier in this post for photos of shaping the dough into rolls.) Repeat with each piece of dough, placing 12 rolls in each pan.
Step 8
Brush the tops of the rolls with some of the melted salted butter and cover with plastic wrap. Let rise for about 1 hour, until the rolls have nearly doubled in size.
Step 9
Preheat the oven to 375 degrees F (190.5 degrees C). Remove the plastic wrap, and bake for 30 - 35 minutes, until they are a rich golden brown. To test for doneness, remove one pan from the oven and insert a knife in-between a couple of the rolls in the center of the pan. Pull the sides of the rolls apart slightly. If they still look doughy, put them back in the oven for another 5 minutes and then check again.
Step 10
Remove the pans from the oven and brush the tops of the rolls with more melted butter. Let cool on a wire rack for 10 minutes before serving. These are best served fresh and warm, but can be stored in an air tight container for up to 2 days.