Preheat oven to 375 degrees.with rack in center. Butter a 10-inch-by-3-inch cake pan. Line the bottom with parchment paper; set aside.
Bring a large pot of water to a boil; add salt. Cook spaghetti, according to package instructions, until al dente. Meanwhile, in a large bowl, combine eggs, mozzarella, soppressata, pecorino Romano, heavy cream, dried parsley, salt, and pepper. Stir to combine. Drain spaghetti, and add to the egg-and-cheese mixture; stir to combine. Pour mixture into prepared pan, and cover with aluminum foil.
Bake about 40 minutes. Remove foil, and bake until lightly browned and crisp on top, 20 minutes more.
Transfer to a rack to cool, about 10 minutes. Run a knife around the edge, and unmold, removing parchment. Invert, cut into wedges, and serve hot.