Peel the mangoes, slice in half and then slice the cut halves lengthwise into thin strips. Set aside.
Using an electric mixer, beat the whipping cream in a medium bowl until double in size. Add condensed milk and vanilla extract; mix until well combined.
Put a layer of graham crackers at the bottom of an 8-inch square glass baking dish or any similar container, filling the gaps with trimmed crackers. Spread 1/3 of the cream mixture evenly on top of the crackers and then top with a layer of mango slices.
Place another layer of graham crackers, cream mixture and slices of mango; repeat the process one more time, ending with slices of mango.
Refrigerate the mango float overnight to set completely before serving.
