Preheat the oven to 400 degrees F. Grease a large baking sheet.
Brown the pork sausage in a skillet until it is no longer pink. Remove the excess grease. Set aside.
In a clean skillet melt the butter and add the onions and peppers. Cook until they start to soften.
In a small bowl add the egg and beat. Pour the eggs over the onions and peppers. Stir the eggs as they begin to set. Cook until the eggs are no longer runny. Take off of heat and set aside.
You can make the dough while the other ingredients are cooking or wait until they are fully cooked.
For the dough add 1 cup of flour to a medium bowl along with the yeast, sugar, and salt and mix well. Add the warm water and olive oil and stir in.
Gradually add the remaining flour until you have a soft dough. Grease the bottom of the bowl and turn the dough over. Let the dough rest for 10 to 15 minutes.
Divide the dough into 6 balls. On a greased surface pat the balls into 8-inch circles. Divide the sausage between the circles of dough using just half of the circle. Top the sausage with the eggs and then the cheese.
Pull the side of the dough that does not have the ingredients over top of the sausage and eggs. Seal the ends with a fork.
Place the calzones on the prepared baking sheet. Place in the oven and bake for 15 to 17 minutes or until lightly browned.