Prep: Line a 9x9" pan with parchment paper on all sides. Use binder clips to secure the parchment paper to the sides of the pan. Set aside.
Cook strawberries: In a small saucepan, add the diced strawberries and a bit of water to help get it started. Cover and bring to a boil. Leave the lid slightly ajar and simmer on medium heat until the strawberries have broken down and the mixture is thick and chunky. Uncover and let most of the water cook off until you have a thick strawberry compote. Transfer it to small bowl to cool completely.
Crush graham crackers: Place the graham crackers in a ziploc bag and smack them with a rolling pin until they become very finely crushed. You can also use a food processor. Transfer the crumbs to a medium bowl.
Crust mixture: Pour melted butter over the crushed graham crackers and mix with a spatula until the crumbs are all saturated and the mixture resembles wet sand. Transfer half of the crumb mixture to your lined pan.
Press into pan: Use a a spatula or the flat bottom of a measuring cup to press the crumbs firmly into an even layer on the bottom of the pan. Let this sit in the freezer while you prepare the ice cream filling. Cover the bowl of remaining crumb mixture and set aside in a warm place.
Whip cream: In a large mixing bowl, add the whipping cream and vanilla extract. Use a whisk to whip the cream until it becomes firm peaks.
Ice cream mixture: Pour the condensed milk into the cream while whisking until combined. Add the cooled strawberry compote and mix until thoroughly combined.
Fill pan: Pour the ice cream mixture into the pan on top of the crust. Cover and freeze for at least 2 hours or until the ice cream layer is firm to the touch.
Final crust layer: Add the remaining crust mixture on top of the ice cream layer. Spread it out evenly and press it down firmly with a spatula or the bottom of a measuring cup. Return it to the freezer and freeze for at least 12 hours or overnight until completely solid.
Slice: Lift the ice cream sandwich block out of the pan by lifting it up by the parchment paper overhangs. Use a large, sharp knife to cut it into 8 bars before serving or returning them to the freezer.