Combine 2 cups flour, water, sourdough starter, butter, sugar, and salt in a bowl. Mix into a stiff batter. Beat for a few minutes using a wooden spoon or an electric mixer; the dough should be quite moist and sticky.
Turn dough into an oiled bowl, flipping to coat all sides. Cover the bowl with a clean towel and leave at room temperature to ferment 8 hours to overnight.
Turn dough onto a liberally floured surface. Knead for at least 10 minutes, adding an additional 1/2 cup flour or more as needed; the dough should be very smooth and elastic when done.
Butter a loaf pan. Shape dough into a loaf and place in the prepared pan. Cover with a clean towel and let rise in a warm place until doubled in bulk, 4 to 12 hours depending on temperature.
Preheat the oven to 350 degrees F (175 degrees C).
Brush the top of the loaf with beaten egg. Cut a 1/4-inch slash down the center lengthwise using a sharp knife.
Bake in the preheated oven until an internal temperature of at least 180 degrees F (82 degrees C) is reached, 25 to 30 minutes.
Turn loaf out onto a rack and cool completely before slicing.
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