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To a large bowl add the cream cheese and sweetened condensed milk. With an electric mixer, whip together cream cheese and sweetened condensed milk until smooth.
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Add instant pudding and milk to the cream cheese mixture. Whip with an electric mixer until smooth and thick.
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Fold in the whipped topping into the cream cheese mixture with a silicone spatula and mix until just combined.
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Lay graham cracker sheets along the bottom of a 9×13 pan to form a full layer. Pour about 1/3 of the cream cheese filling over the graham crackers and smooth with a spatula until even. Add a single layer of strawberry slices over the cream cheese filling in the pan.
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Repeat the layering of graham crackers, cream cheese filling and strawberries two more times, each time using 1/3 of the cream cheese mixture. On the top cream cheese mixture, add the prettiest strawberry slices for the last layer.
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Refrigerate the icebox cake for 6-8 hours or overnight. Graham crackers will be soft, and the cream cheese mixture will have thickened and become more firm. Slice the cake and enjoy!