Add the first 5 ingredients to a 1-1/2- or 2-pound bread machine according to the manufacturer's directions. Select the dough cycle. When cycle is complete, remove dough from machine. Punch down. Cover and let rest for 10 minutes.
Meanwhile, for filling, in a large skillet cook the sausage over medium heat until brown. Drain off fat, reserving about 1 tablespoon drippings in skillet. Add the mushrooms and onion. Cook and stir over medium heat until vegetables are tender. Drain off any liquid. Stir in the pizza sauce and roasted peppers. Set aside.
Grease bottom and side of a 9x3-inch springform pan. Shape one-fourth of the dough into a small ball. Shape the remaining portion of dough into a large ball. On a lightly floured surface, roll the large ball into a 16-inch circle. Fit dough into the bottom of the prepared pan; press dough up the side of the pan, allowing dough to extend slightly over edge for easier filling. Sprinkle with half of the cheese; top with meat mixture. Sprinkle with the remaining cheese; press lightly into meat mixture.
Roll the small ball into a 9-inch circle; place on top of meat mixture. In a small bowl combine the egg and 1 tablespoon water; brush over dough. Fold edge of bottom dough over top dough; press lightly to seal. Brush again with egg mixture; cut slits in dough. Sprinkle with sesame seed.
Bake in a 350 degree F oven for 45 to 50 minutes or until golden brown. Cool in pan on a wire rack for 20 minutes. To serve, use a metal spatula to loosen the pie from edge of pan; remove side of pan. Cut into wedges.