For the Cheesecake Ice Cream:

1. Prepare the Cream Cheese Base:
   In a large mixing bowl, beat the softened cream cheese until smooth. Add the sweetened condensed milk and mix until well combined.
2. Whip the Cream:
   In a separate bowl, whip the heavy whipping cream to soft peaks. Gently fold the whipped cream into the cream cheese mixture until fully incorporated.
3. Freeze the Ice Cream:
   Pour the cheesecake ice cream mixture into a freezer-safe container. Freeze for at least 4 hours or until firm, preferably overnight.

For the Red Velvet Cake:

1. Preheat Oven:
   Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
2. Mix Dry Ingredients:
   In a medium bowl, whisk together the flour, cocoa powder, and salt.
3. Cream the Butter and Sugar:
   In a large mixing bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, followed by the vanilla extract.
4. Prepare the Batter:
   In a small bowl, mix the red food coloring with the buttermilk. Gradually add the flour mixture and buttermilk mixture to the creamed butter, alternating between the two until combined.
5. Activate Baking Soda:
   In a small bowl, mix the vinegar and baking soda (it will fizz). Quickly fold this mixture into the batter.
6. Bake:
   Divide the batter evenly between the prepared cake pans. Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely.

Assemble the Cake:

1. Layer the Cake and Ice Cream:
   Once the cake layers are completely cooled and the cheesecake ice cream is firm, place one layer of the red velvet cake on a serving plate. Spread a thick layer of cheesecake ice cream on top of the cake layer, smoothing it out evenly.
2. Top with Second Cake Layer:
   Gently place the second red velvet cake layer on top of the ice cream layer.
3. Freeze:
   Freeze the assembled cake for at least 2-3 hours to ensure it sets properly.

Serve:

1. Before serving, let the cake sit at room temperature for 5-10 minutes to soften slightly for easier slicing.
2. Optionally, decorate the top with whipped cream, cream cheese frosting, or a dusting of cocoa powder.