Using an electric mixer, beat the cream, condensed milk, and vanilla in a large bowl on medium-high until stiff peaks form, 3 to 4 minutes.
With the mixer running, toss the cream cheese by the teaspoonful into the batter and allow it to incorporate.
Gently fold in the strawberries and graham crackers, reserving some for the topping. Mix until incorporated.
Spoon the cream mixture into a 4 1/2- by 8 1/2-inch loaf pan or 1 1/2-quart freezer-safe container. Sprinkle the reserved strawberries and graham crackers on top. Freeze until set, at least 4 hours.
Once set, cover with plastic wrap and freeze for up to 2 weeks.