Gently warm the buttermilk until it is just lukewarm (body temperature) and dissolve the yeast in it - this is easiest with a whisk. Then add the egg and sugar.Take care not to heat the buttermilk over too high a heat or to too high a temperature, or it will go lumpy.
Mix the flour and salt and add it a little at a time, mixing the dough, ideally in a stand mixer, until all the flour is worked into the dough.
Add the butter in small cubes and knead the dough thoroughly until it comes together and pulls away from the sides of the bowl.
Take the dough out of the bowl, tighten it slightly by folding the edges in under the base, and shape it into one large ball. Put it back in the proving bowl and dust with a little flour if you like.
Cover the bowl with cling film and a tea towel and leave the dough to rise in a warm place for about 1 hour.
Divide it into 12 equal pieces, about 75 g each, and roll them into round rolls. Tighten each piece by folding the dough in under the roll until the surface is smooth, then roll it round between your palms.
Place them on a baking tray and leave them to prove for about 30 minutes under a tea towel. You can place them close together so they join up as they bake, or well spaced out - it is up to you.
Brush the rolls with beaten egg and bake them in a preheated oven at 225°C, conventional oven (top and bottom heat), for about 12 minutes.Let the rolls cool on a wire rack before packing them in an airtight bag, and store them at room temperature - they will stay soft for several days.