In a mixing bowl, whisk cream, milk, sugar, and vanilla until sugar is dissolved. Chill for 1 hour.

In a saucepan, simmer black raspberries with 2 tbsp sugar and lemon juice until thickened (about 6 minutes). Cool completely.

Churn the cream mixture in your ice cream maker as directed.

Layer churned ice cream with spoonfuls of black raspberry sauce and crushed Oreos in a freezer-safe container.

Swirl gently with a knife. Freeze for at least 4 hours or overnight.