Begin by preparing the crust and softening your ice cream. Remove 1 3/4 quarts of Breyer's strawberry ice cream (or approximately 1/2 gallon of other premium ice cream) from the freezer and set it on the counter for 30 minutes to thaw.
While the ice cream softens, prepare the graham cracker crust by combining 1 1/2 cups of finely ground graham cracker crumbs, 6 tablespoons of melted salted butter, and 1/4 cup of sugar in a bowl and mixing with a fork until the mixture resembles wet sand.
Transfer this mixture to a 9-inch springform pan and press it firmly over the bottom and slightly up the sides using your fingers. Use the bottom of a glass to flatten and compact the crust, then set the pan aside.
Once the ice cream has reached a soft but not melted consistency, transfer it to a large bowl and mix thoroughly with a wooden spoon until smooth and creamy (alternatively, use a mixer with a paddle attachment for easier blending).
Break the store-bought cheesecake (8-9 inches with graham cracker crust), which should be at room temperature, into manageable pieces and gently fold them into the softened ice cream until evenly distributed throughout. Pour the ice cream and cheesecake mixture onto the prepared crust in the springform pan, smoothing out the top with a spatula to create an even layer.
Place the assembled dessert in the freezer and allow it to set for four hours until completely frozen and firm. When you're ready to serve, remove the sides of the springform pan and let the cheesecake ice cream sit on the counter for approximately 15 minutes before slicing—this resting period allows the dessert to soften slightly, making cutting cleaner and easier.
Serve each slice topped with thawed sweetened strawberries and their juice for an elegant finishing touch.