Cookie Dough Ice Cream Cake

To Make Hot Fudge Sauce: Combine chocolates, corn syrup, brown sugar, cream, butter, and salt in a heatproof bowl or in the top of a double boiler. Bring 2 inches water to boil in a saucepan or bottom of double boiler. Remove pan from heat, place bowl with chocolate mixture over hot water, and let stand, stirring occasionally with a flexible spatula, until mixture is melted and smooth, about 15 minutes. Stir in vanilla. Tightly covered, the sauce will keep about 2 weeks in the refrigerator. Warm it in the microwave or in a bowl set over a pan of hot water before serving. To Make Chocolate Chip Blondie: Preheat oven to 325 deg F. Butter and flour a 10-inch springform pan. In a bowl, with an electric mixer, beat butter, brown sugar, and granulated sugar until blended and smooth. Beat in eggs and vanilla until well blended, scraping down sides of bowl as necessary. In another bowl, stir together flour, baking powder, baking soda, and salt. Stir half the flour mixture into butter mixture. Stir in milk, followed by remaining flour mixture, just until well blended. Stir in chocolate chips. Spread batter evenly into pan and bake until skewer inserted into the center comes out clean, 45 to 50 minutes. Remove pan rim and cool cake completely on a wire rack. Halve blondie horizontally with a serrated knife. Remove top layer, leaving bottom half of the cake on the pan base. Replace pan rim around cake but do not close it tightly. Line the inside of the pan rim with strips of parchment or waxed paper wide enough to come slightly above the top of the rim; tighten rim around the cake. Soften ice cream, and spread on bottom layer, smoothing the top. Place top layer of blondie over ice cream, compressing slightly. Cover with plastic wrap and freeze until firm, at least 8 hours and up to 2 days. To serve, remove ice cream cake from freezer and remove plastic wrap, pan rim, and parchment strip. Let cake stand at room temperature 5 to 10 minutes. To slice cake neatly, dip the blade of a large, sharp knife in hot water and wipe it dry before cutting each slice. Serve immediately.