Bread machine: Mix flour, sugar, pepper flakes and salt in a bowl. Whisk water eggs and melted butter together. Add liquid to bread machine, then dry ingredients, then top with yeast. Set bread machine to dough cycle.Stand mixer: Mix all dry ingredients (excluding Toppping ingredients) in bowl of your mixer. Mix all wet ingredients together. Stir wet mixture into the dry mixture in the bowl. With dough hook, knead on medium for 9 minutes. Dough will form a ball and clear sides and bottom of bowl. Transfer dough to a greased ball, shaped in a ball. Cover with plastic wrap and allow to rise 1 ½ hours until doubled in size.
Cut cheese in to ½" cubes and allow to come to room temperature while dough is rising.
Grease and line a round baking pan 7-9" in diameter, with parchment paper.
Transfer dough to working surface. No need to flour surface, the dough is soft and pliable. Roll out to 18 X 12" rectangle. Distribute the cheese cubes evenly over the dough leaving a 1" border free around the edges.
Roll the dough along the long side, tightly in to a log. Pinch the ends to seal them. Gently roll, massage the dough log until it reaches 30" inches. Pinch any tears in the dough to seal.
Coil the dough log in to your prepared baking pan. Cover loosely with a towel and allow it to rise 1 ½ hours until doubled in size.
Heat oven to 350° near the end of the second rise. Brush to top of the loaf with the egg and then sprinke with the red peppers. Place baking sheet on a baky tray to catch any oozing cheese. Bake 25 minutes and then tent with aluminum foil. Bake a further 25-30 minutes until internal temp reaches 190°.
Remove pan from the oven and brush the top with the soft butter. Allow loaf to cool 10 minutes in the pan and then loosen the loaf and all it to cool another 30 minutes on a wire rack.
Serve warm.
To store refrigerate, well sealed. Reheat gently if desired. It is also delicious toasted in a panini maker or grill pan.