Unfold pastry sheet onto a lightly floured surface. Roll into a 13" square. Place in a lightly greased 9" deep-dish pieplate. Fold edges under, and crimp. Prick pastry lightly with a fork. Freeze at least 15 minutes to make pastry firmer. Bake pastry at 400° for 12 minutes. Let cool on a wire rack.
Reduce oven temperature to 350°. Cook spinach according to package directions. Squeeze spinach between several layers of paper towels to remove excess moisture. Combine spinach, cream, salt, 1/2 teaspoon pepper, and eggs, stirring well.
Sprinkle mozzarella and Cheddar cheeses and onion into pastry shell. Add spinach mixture. Top with red pepper; sprinkle with feta cheese. Bake, uncovered, at 350° for 55 minutes or until set. Cover loosely with aluminum foil, and let stand 30 minutes before serving.
Note: You can use 1/2 (15-ounce) package refrigerated piecrusts instead of puff pastry in this quiche, but it won't be as flaky.