In a large mixing bowl, stir together 4 1/2 cups all-purpose flour, 1/2 teaspoon baking soda, and 4 1/2 teaspoons active dry yeast. Set aside.
In a large saucepan, combine 1 1/2 cups full-fat buttermilk, 1/2 cup salted butter, diced, 3 tablespoons granulated sugar, and 2 teaspoons salt. Heat on low until the buttermilk is warm but not boiling. It should stay between 110-115 degrees Fahrenheit. The butter may not be completely melted at this point, which is fine.
Stir the buttermilk mixture into the flour mixture. If you are using a stand mixer, use the dough hook and mix until the dough is a large ball. If doing it by hand, stir using a wooden spoon until the dough is smooth.
Cover and let rise for 60 minutes. It should double in size.
Punch the dough down and gently knead on a floured surface until smooth.
Divide the dough in half. Set aside one half for now.
With the other half, flatten slightly and divide into 6 equal parts. Divide each section into 3 or 4 pieces and roll them into balls. Repeat the process until all the dough is in small balls.
Place 3 or 4 of the small dough balls into each muffin cup. Cover the muffin tin for another 60 minutes. It will continue rising in the pan.
Preheat the oven to 375 degrees F. In a small mixing bowl, combine 1 large egg and 1 tablespoon water. Lightly beat them together.
Brush the egg mixture onto the tops of the dough.
Bake for 18-20 minutes or until the buns are golden brown.
Notes
Tip: Keep the warmed buttermilk/ butter mixture between 110-115 degrees Fahrenheit. This will activate the yeast without killing it. Too cold, you won't get any rise; too hot, and it will destroy the yeast. If you don't have a thermometer, a good rule of thumb is to be able to stick your finger in it without burning yourself, but you shouldn't keep it in longer than 5-8 seconds. It's a crude way of doing it, but it will work.
Making in advance: You can freeze the dough or refrigerate it for a day or two before baking these rolls. Please see the tips section at the bottom of the post for instructions.