If you have a bread-proof feature on your oven, turn it on. Otherwise, you will need a clean kitchen towel and warm water.
Butter a 9-by-5-by-3-inch loaf pan, using 1 tablespoon of the butter. In a large mixing bowl (or in the bowl of a stand mixer), combine 1 ½ cups of the flour with the sugar, salt, and yeast. In a small saucepan, heat the buttermilk and 2 tablespoons of the butter over medium heat until the butter is melted and the mixture reaches about 130 degrees Fahrenheit on an instant-read thermometer . The mixture should be warm, but not hot to the touch. Remove from the heat.
Using a stand mixer fitted with the flat beater or a simple kitchen fork and mixing bowl, add the warm buttermilk mixture to the flour mixture and combine until just incorporated. Dough will be stringy.
Add the egg and stir 1 minute more.
Add the remaining 1 3/4 cups flour and continue mixing until mostly incorporated. Knead in the bowl or on a board for 2 to 3 minutes. This dough tends to be stringy and sticky. Wet your hands to knead if necessary versus adding any additional flour.
Transfer the dough into the prepared loaf pan or Pullman pan and spread it out to the corners.
Cover loosely with a clean, warmly dampened dishtowel or secure the top of the Pullman pan and place in a bread proof mode warm oven and let rise about 1 hour to 1 hour and 15 minutes. I place mine in my oven on bread-proof mode, door closed, and this gives way to a nice speedy rise. If your oven does not feature a bread-proof mode, turn the oven light on and close the door. The heat from the lamp will be enough to aide in the rise.
When dough has risen sufficiently, remove the loaf pan. Preheat your oven to 375°F. Make a shallow cut lengthwise down the center of the loaf or two parallel cuts, whichever you prefer. If using a Pullman pan there is no need for a cut.
Melt the remaining tablespoon of butter and brush it over the loaf.
Place a foil catch beneath the loaf pan and on top of a baking sheet for easy handling. This will prevent any spillover of the butter.
Bake in the center of the preheated oven for 30 to 35 minutes, until the top is firm and lightly browned. Loaf will sound hollow when you tap it. Place the pan on a wire rack and let cool 10 minutes. Remove bread from pan and cool slightly on the rack before slicing.
Serve warm with salted sweet cream butter, an herby compound butter, a drizzle of salted honey, or a spoonful of homemade jam. This bread, sliced thin, also makes a truly ultimate grilled cheese sandwich.