Cut a 24-by-6-inch strip of parchment paper. Butter the side of an 8-inch springform pan, then line the side with the parchment; the paper will extend above the rim of the pan so you can build a tall cake. Cover the bottom of the pan with half of the pizzelle cookies, breaking them into smaller pieces as needed to cover the surface. Spread 1/4 cup fudge sauce over the cookies. Pack about half of the vanilla-caramel and chocolate ice cream into the pan, alternating scoops of each flavor, until the bottom is covered. Drizzle with 1/4 cup dulce de leche and sprinkle with 1/4 teaspoon sea salt. Top with the remaining pizzelle cookies, pressing gently to pack in the ice cream and create an even surface. Spread 1/4 cup fudge sauce over the pizzelle cookies. Top with scoops of the remaining vanilla-caramel and chocolate ice cream. Drizzle with the remaining 1/4 cup each dulce de leche and fudge sauce and sprinkle with the remaining 1/4 teaspoon sea salt. Arrange the ice cream cones, point-side up, on top. Freeze until firm, at least 6 hours or overnight. Remove the side of the springform pan and the parchment. Press the toffee bits into the side of the cake. Serve immediately or freeze for up to 2 days.