In a medium saucepan, combine the 480 g (2 cups) whole milk, 360 g (1½ cups) heavy cream, 140 g (⅔ cup) granulated sugar, 30 g (⅓ cup) nonfat dry milk powder, 15 g (1 tablespoon) light corn syrup, and ⅜ teaspoon fine salt.

Heat over medium heat until steaming but not boiling.

In a medium bowl, whisk the 4 egg yolks.

Slowly pour the hot milk mixture into the yolks while whisking constantly.

Return the mixture to the saucepan and cook over medium-low heat, stirring constantly, until it reaches 170–175°F (77–79°C).

Remove from the heat and stir in the 1½ teaspoons vanilla bean paste, 1 teaspoon vanilla extract, ½ teaspoon almond extract, and optional 1–2 drops butter extract.

Cover and refrigerate overnight.

In a medium bowl, beat together the 60 g (¼ cup) cream cheese, 90 g (⅓ cup) marshmallow fluff, 1 teaspoon vanilla extract, tiny drop almond extract, and pinch of salt until smooth.

Mix in the 85 g (3 oz) melted white chocolate until fully combined.

In a separate bowl, whip the 180 g (¾ cup) heavy cream to medium peaks.

Fold the whipped cream into the cream cheese mixture until no streaks remain.

Cover and refrigerate overnight.

Place a 6-inch cake ring or springform pan on a parchment-lined cake board or sheet pan.

Line the inside of the pan with acetate and tape the seam together.

Because this cake is tall, stack a second strip of acetate above the first and tape it securely in place to create taller sides.

Churn the chilled ice cream base according to your ice cream maker's instructions until thick and soft-serve-like, about 25 minutes.

Fold in the 4–6 chopped frosted sugar cookies.

Arrange about 5–6 frosted sugar cookies across the bottom of the prepared pan.

Fit the cookies together like a puzzle or mosaic, breaking pieces as needed to fill gaps and create an even layer.

Freeze for 5–10 minutes.

Spread about one-third of the ice cream evenly over the cookie layer.

Freeze for 20 minutes.

Arrange another layer of about 5–6 frosted sugar cookies over the ice cream, fitting them together like a mosaic and filling any gaps with broken pieces.

Freeze for 5–10 minutes.

Spread the frosting mousse evenly over the cookie layer.

Freeze for 20 minutes.

Spread another one-third of the ice cream over the mousse layer.

Freeze for 20 minutes.

Arrange a third cookie layer using about 5–6 frosted sugar cookies, again fitting the cookies together like a puzzle and filling gaps with smaller pieces.

Freeze for 5–10 minutes.

Spread the remaining ice cream evenly over the cookie layer.

Freeze for 20 minutes.

Arrange the remaining frosted sugar cookies over the top of the cake in a decorative mosaic pattern.

Freeze overnight or until completely firm.

Remove the cake from the freezer and let sit at room temperature for 8–12 minutes.

Remove the cake ring and carefully peel away the acetate.

Heat a large chef's knife in hot water, wipe completely dry, and slice. Wipe and reheat the knife between cuts for the cleanest slices.