Make the spinach layer: In a large skillet, heat oil over medium heat. Add onion and cook until translucent, about 5 minutes. Add garlic and stir for one minute. Add spinach, basil, salt and pepper. Cook, stirring constantly, until moisture evaporates from spinach and spinach begins to stick slightly to skillet, about 5 minutes. Transfer to a medium bowl and cool completely.
Make the egg layer: In a large bowl, whisk eggs, salt and pepper until well combined. In a medium skillet, preferably non-stick, heat one tablespoon oil over medium heat. Add half of the egg mixture and cook, stirring often until eggs are soft-set, about 1-1/2 minutes. Transfer to another bowl. Repeat procedure with remaining oil and eggs. Set aside to cool completely.
Position a rack in the center of the oven and place a baking sheet on the rack. (The baking sheet is important as it helps set the bottom crust and catches any dripping butter from the cooking pastry.) Preheat oven to 425°F.
Lightly butter the inside of a 9-inch round spring form pan. Tightly wrap bottom of pan with a double thickness of aluminum foil.
Torte Rustic continued:
On a lightly floured work surface, roll out one sheet of puff pastry to 1/8-inch thickness. Carefully transfer pastry to prepared pan ? pressing dough against sides of pan and letting excess pastry hang over edges. Brush inside of dough lightly with some of the beaten egg white.
Sprinkle dough with half of the Parmigiano Reggiano and Gruyere cheese. Layer with half of the smoked ham, then half of the peppers. Spread with half of the spinach mixture, then half of the beaten eggs. Repeat with remaining ingredients.
Roll out remaining sheet of pastry to 1/8-inch thickness. Center the pastry on top of filling. Cut a small hole out of the center of the pastry to allow steam to escape. Press layers of dough together firmly around edges of spring form pan. With a sharp knife or scissors, trim away excess dough at pan?s edge, leaving a 1/2 inch wide border of dough. (If desired, reserve pastry trimmings and cut out decorations). Roll up dough into a thick rope and pinch and flute with fingers to seal. Brush top of dough lightly with some of the yolk glaze. If using, place pastry decorations on top and brush decorations lightly with glaze.
Place spring form pan on preheated baking sheet in oven. Bake for 10 minutes. Reduce heat to 325°F and continue baking until golden brown, 50 minutes to 1 hour.
Cool completely in pan on a wire rack. (The torte can be prepared up to 2 days ahead, cooled, covered tightly with foil and refrigerated). Remove sides of pan. Use a serrated knife to cut into wedges and serve at room temperature.