We unmolded the pie onto a serving platter. For a less formal presentation, you can simply cut wedges directly from the baking dish.
Preheat oven to 375 degrees with a rack in the center. Butter a 10-by-3-inch round cake pan. Line the bottom with parchment paper, and butter parchment.
In a large bowl, combine eggs, mozzarella, soppressata, Pecorino Romano, heavy cream, parsley, and 1/2 teaspoon pepper; season with salt, and stir to combine. Add spaghetti, and stir to combine. Pour mixture into prepared pan.
Cover pan with foil, and place in oven. Bake until pie is heated through and beginning to bubble, about 40 minutes. Remove foil, and bake until lightly browned and crisp on top, about 20 minutes more.
Transfer pan to a wire rack; let cool 10 minutes. Run a knife around the edge, and invert onto a large plate. Remove parchment paper, and reinvert onto a serving platter. Cut into wedges; serve.