Cherry-Cheesecake Celebration Bombe

Sponge Cake: Preheat oven to 350°F. Brush a 10-inch round cake pan with oil. Line bottom with parchment; brush parchment. Whisk together flour, salt, and baking powder to combine. In a large heatproof bowl, whisk hot water with 1/4 cup granulated sugar until dissolved. Whisk in oil, then egg yolks and vanilla until smooth. Whisk flour mixture into oil mixture just until combined.

In a mixer fitted with the whisk attachment, beat egg whites on medium-low speed until frothy. Add cream of tartar, increase speed to medium-high, and continue beating until soft peaks form. Gradually add remaining 2 tablespoons granulated sugar; continue beating until stiff, glossy peaks form, about 2 minutes. Stir one-third of egg whites into batter. Gently fold in remaining egg whites just until no streaks remain. Transfer to prepared pan, smoothing top with an offset spatula.

Bake until cake is pale golden and top springs back when lightly pressed, 15 to 17 minutes. Let cool 15 minutes in pan on a wire rack, then turn cake out onto rack, remove parchment, and let cool completely.

Cherry-Cookie Crumb: Pulse cookies, cherries, and granulated sugar in a food processor until finely ground. Add butter; pulse until texture resembles wet sand (you should have 2 packed cups). Transfer to a bowl, or refrigerate in an airtight container up to 1 week.

Cream-Cheese Filling: Line a 10-inch-diameter mixing bowl (10-to-12-cup volume) with plastic wrap, leaving a long overhang on all sides. Beat cream cheese on medium-high until light and fluffy, about 2 minutes. Beat in condensed milk. In another bowl, whisk cream and vanilla to soft peaks. Fold into cream-cheese mixture to combine. Transfer to prepared mixing bowl, smoothing top with an offset spatula. Sprinkle evenly with 1 cup cookie-crumb mixture. Transfer to freezer.

Cherry Ice Cream: Combine cherries, corn syrup, and cornstarch in a medium saucepan. Bring to a boil, stirring a few times. Boil until juices thicken slightly, about 1 minute. Transfer to a bowl and refrigerate until cool, about 30 minutes (or cool quickly over an ice-water bath). Temper ice cream in refrigerator until softened but not melting, about 20 minutes.

Transfer ice cream and chilled cherry mixture to a food processor. Pulse just until combined and no streaks of ice cream remain. Pour into bowl in freezer, smoothing top. Top with sponge cake. Cover cake with plastic over-hang and freeze until firm, at least 8 hours and up to 5 days.

Dip bowl in a hot-water bath 10 seconds. Wipe bowl dry and invert onto a cake plate. Remove bowl and plastic wrap. Using your hands, press remaining cookie-crumb mixture evenly over cream-cheese filling (remove any crumb mixture that falls onto plate with a pastry brush). Cut into wedges and serve immediately, or wrap in plastic and return to freezer until ready to serve, up to 3 days.