Preheat the oven to 350 degrees.
In a large skillet, heat the first 5 ingredients until the sausage is no longer pink. The vegetables should be tender. It will take about 6-8 minutes.
Add the cream cheese, green onion, and parsley. Stir it over low heat until the cream cheese has melted.
Unroll the crescent dough onto a greased baking sheet. Press the perforated edges together to form the dough into a 12x10 inch rectangle.
Spoon the sausage mixture lengthwise down the center third of the rectangle.
On each side of the sausage mixture, use scissors to cut 1-inch rectangles toward the center. Leave about 1/2-1 inch of space between the end of the cut and the sausage mixture.
Fold alternating strips of dough over the sausage from right to left to right again, all the way down the braid. Press to seal the ends.
Brush the egg mixture on top. Bake at 350 degrees for 20-25 minutes or until golden brown.