Activate the Yeast: In a large mixing bowl, combine the warm milk, 2 tablespoons of granulated sugar, and the active dry yeast. Whisk gently and let it sit for about 5 minutes until it becomes nicely foamy. This means your yeast is active and ready to make some fluffy rolls!
Mix the Dough: Add 2 ½ cups of the flour, the sea salt, 6 tablespoons of softened butter, the remaining 2 tablespoons of sugar, the whole egg, and the egg yolk to your yeast mixture. If using a stand mixer, attach the paddle and mix on the lowest speed until everything is just combined. Scrape down the sides, then increase to medium-low speed and mix for another 2 minutes.
Knead to Perfection: Switch to the dough hook attachment. Add ½ cup of flour and mix on the lowest speed until almost fully incorporated. Then, increase to medium speed for about 2 minutes. Repeat this step with another ½ cup of flour, mixing until a soft, slightly sticky dough ball forms. The dough should pull away from the bowl's edges but still stick a bit to the bottom. Avoid adding too much flour; a sticky dough makes for tender rolls!
First Rise: Lightly grease a clean bowl with cooking spray. Transfer the dough, cover it with a towel or plastic wrap, and let it rise in a warm, draft-free spot until it has doubled in size. This usually takes about 45 to 90 minutes.
Prepare for Shaping: Once risen, gently punch the dough down to release the air. Divide the dough in half and place one half on a very lightly floured surface. Remember, less flour is key for soft rolls!
Roll and Butter: Roll or pat out the dough into a rectangle, roughly 8 inches by 12 inches (about the size of a piece of printer paper). Brush this rectangle evenly with 2.5 tablespoons of the softened butter.
Fold and Cut: Cut the buttered dough rectangle lengthwise into two 4x12 inch pieces. Take one piece and fold it lengthwise, leaving about ½ inch of the far edge showing. This creates the classic Parker House "purse" shape. Cut this folded piece into four equal 3-inch segments. Repeat with the second 4x12 inch piece, so you have 8 shaped rolls from this first dough half.
Arrange and Repeat: Lightly grease a 9x13 inch baking dish. Place the shaped rolls, folded side down, in rows (4 rolls per row, with longer sides parallel to the dish's longer side). Repeat steps 6 and 7 with the second half of your dough, filling the rest of your baking dish. You should have 16 rolls total.
Second Rise & Preheat: Cover the baking dish again with a towel or plastic wrap. Let the rolls rise for about 45 minutes to 1 hour, until they look nicely puffed up. Towards the end of this rise, preheat your oven to 350°F (175°C).
Bake and Finish: Remove the cover from the rolls and bake them for 20 to 25 minutes, or until they turn a beautiful golden brown. As soon as they come out of the oven, brush the tops generously with the remaining 2.5 tablespoons of softened butter. Serve warm and enjoy these irresistible, pull-apart rolls!