Roll out 1 half on a lightly floured surface into a 10-inch circle. Cover, and set aside.
Press together remaining 1 1/2 dough loaves, and roll out onto a lightly floured surface into a 12-inch circle. Fit dough into a 9-inch springform pan, allowing edges to overhang.
Drain spinach, artichokes, red pepper strips, and olives. Press spinach and red pepper strips between layers of paper towels, and set aside.
Saut mushrooms in a nonstick skillet 8 minutes; drain.
Layer half of salami, mushrooms, and olives in dough-lined pan; top with half of cheese slices.
Layer with half of ham, spinach, pepper strips, remaining salami, remaining ham, and artichokes; top with remaining cheese slices.
Stir together egg and water; brush on overhanging pastry edges. Top torte with remaining pastry round. Fold overhanging edges over top pastry, crimping as necessary, and press to seal.
Brush top with remaining egg mixture.
Bake at 350 on bottom oven rack 30 to 35 minutes.
Remove from oven, and cover with aluminum foil, if necessary, to prevent excessive browning.
Bake 15 to 20 more minutes. Cool in pan on a wire rack.
