Begin by putting the buttermilk, 4 tablespoons of butter, honey, and salt into a small pot. Cook on low until the honey dissolves and butter melts. (Make sure that the mixture doesn’t get hotter than 100° F. )
Pour the buttermilk mixture into a large bowl. Add the eggs and the sourdough and mix until smooth.
Set 1⁄2 cup of flour aside and add the remaining 3 1⁄4 cups to the bowl. Mix until you have a stiff, tacky dough.
Dust a clean work surface with the reserved ½ cup flour and knead the dough until it is smooth and pliable, then form it into a ball and put it into a clean, greased bowl.
Cover the bowl and set it in a warm place for 2 hours.
Butter a 9×13 glass pan or a large cast-iron skillet.
Punch down the dough and divide it into 12 equal portions. Form each portion into a ball and set it in the baking dish.
Once all 12 rolls are formed, cover the dish and let them rise for 2 hours in a warm place, or until the rolls are level with the top of the baking dish.
Preheat the oven to 350° F and melt the remaining 4 tablespoons of butter. Brush the tops of the rolls with about half of the butter.
Bake for 35-40 minutes, until the rolls are golden brown, then take the rolls out and brush them with the rest of the butter.