Prepare Water and Butter: Begin by placing 1 1⁄2 cups of water and 2 tablespoons of butter in a microwave-safe bowl and heat until hot (125°F to 130°F). Set this mixture aside.

Mix Dry Ingredients: In a food processor, combine the all-purpose flour, bread flour, yeast, kosher salt, and 1 tablespoon sugar. Blend these dry ingredients well.

Combine Wet and Dry Ingredients: With the food processor running, slowly pour the hot water and melted butter through the feed tube until you form a smooth dough. Process for about 1 minute to knead.

First Rise: Grease a large bowl with butter and place the dough inside, turning it to coat. Cover with plastic wrap and a towel, letting it rise in a warm area until it has doubled in size (about 1 hour).

Prepare Baking Sheet: While the dough is rising, line a baking sheet with parchment paper and set it aside.

Shape the Rolls: Once risen, punch down the dough and knead it on a floured surface until smooth. Divide the dough into 8 equal pieces and shape each piece into a ball, flattening each slightly.

Second Rise: Cut an 'X' in the top of each dough ball and cover them with a towel, letting them rise again until nearly doubled (about 1 hour).

Preheat Oven: Preheat your oven to 375°F. Prepare another baking sheet with parchment paper and sprinkle it with cornmeal.

Boil the Rolls: In an 8-quart pot, bring 8 cups of water to a boil and add the baking soda and 2 tablespoons of sugar. Gently lower 4 rolls at a time into the boiling water and cook for 30 seconds on each side using a slotted spoon. Transfer each roll to the prepared baking sheet, ensuring the 'X' side is facing up.

Brush and Bake: Brush the rolls with the beaten egg and sprinkle with coarse salt. Bake for about 25 minutes or until golden brown. Transfer them to a cooling rack and allow to cool for 10 minutes.