In a medium bowl, combine the prosecco and strawberries. Let sit for 1 hour.
Strain the prosecco from the strawberries. Add the prosecco and most of the strawberries to the blender, reserving a few strawberries for garnish. Add the strawberry ice cream and blend on high speed until smooth.
Divide the milkshake between 2 glasses, top with the whipped cream, and garnish with the prosecco-soaked strawberries.
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