Prepare hot roll mix according to package directions through the kneading step. Cover; let dough rest for 5 to 10 minutes.
In a large skillet, cook sausage over medium heat until meat is brown. Drain, reserving 1 tablespoon drippings in skillet. Add mushrooms, onion, sweet pepper, and garlic to skillet. Cook over medium heat until vegetables are tender. Drain off any liquid. Stir in pizza sauce. Set mixture aside.
Preheat oven to 350 degree F. Grease the bottom and side of a 9-inch springform pan. On a lightly floured surface, roll three-fourths of the dough into a 15-inch circle. Fit into the bottom and press up the side of the springform pan. Sprinkle bottom of the dough with 1/2 cup of the cheese. Spoon meat mixture over cheese. Sprinkle remaining 1-1/2 cups cheese over meat. Press lightly into meat filling.
On a lightly floured surface, roll the remaining dough into a 9-inch circle; place on top of meat-cheese mixture. Fold edge of bottom dough over top dough; pinch to seal.
In a small bowl, beat together egg and the water. Brush top of pie with egg-water mixture; allow to dry for 5 minutes. With a sharp knife, score top of pie in a diamond pattern, being careful not to cut all the way through the dough.
Bake for 45 to 50 minutes or until golden brown. Cool in pan on a wire rack for 20 minutes.
To serve, use a small spatula or table knife to loosen pie from side of pan; remove side of pan. Cut pie into wedges. Makes 8 servings.