Preheat oven to 350°F (175°C). Grease and line a 9-inch springform pan. Whisk melted butter and sugar, then add eggs, vanilla, cocoa, flour, and salt. Pour into the pan, bake 20–22 minutes until set. Cool completely.
Whisk cream, milk, sugar, cocoa, vanilla, and salt until smooth. Churn until soft-serve texture. Spread over brownie base and freeze 2–3 hours.
Simmer strawberries, sugar, and lemon juice for 6–8 minutes until thick. Let cool.
Blend cream, milk, sugar, strawberry purée, vanilla, and lemon juice. Churn, then layer over chocolate ice cream. Swirl in some sauce. Freeze 2–3 hours.
Whisk cream, milk, sugar, and vanilla. Churn until thick. Spread over strawberry layer and freeze overnight.
Run a warm knife around the pan and release the cake. Top with whipped cream, berries, chocolate shavings, or sprinkles. Slice with a hot knife and serve.