Add the heavy whipping cream to a deep mixing bowl. Using a hand mixer or stand mixer, beat at high speed for about 4-5 minutes, or until stiff peaks form and the cream is light and fluffy. (It should resemble whipped cream.)
2 1/2 cups heavy whipping cream
In another bowl, mix the condensed milk, cream cheese and vanilla paste until smooth. Add the mixture to the whipped cream. Mix at low speed just until fully combined and smooth. (Taste the mixture and, if you prefer a sweeter ice cream, mix in a little more condensed milk.)
8 oz cream cheese, softened, 3/4 cup condensed milk, 1 Tbsp vanilla bean paste, or vanilla extract
Pour about 1/3 of the ice cream mixture into an ice cream container, loaf pan, or metal bread pan.
Add dallops of the strawberry compote over the ice cream. Using a butter knife or fork, gently swirl the compote into the ice cream. (Avoid overmixing so you can still see ribbons of strawberries.)
Sprinkle with crushed graham crackers.
Repeat the layering process 2-3 more times until all the ice cream mixture has been used. Smooth the top layer with a spatula, then sprinkle with the remaining strawberry compote and crushed graham crackers. Gently swirl the top layer.
Press a piece of parchment paper or plastic wrap directly onto the surface of the ice cream to help prevent ice crystals and freezer burn, then cover tightly with a lid or foil.
Freeze for at least 8-12 hours, or overnight, until the ice cream is fully firm and scoopable.
When ready to serve, let the ice cream sit at room temperature for 4–5 minutes to soften slightly. Scoop into bowls or cones and enjoy. (For easier scooping, dip your ice cream scoop into hot water and wipe it dry before each scoop.)