Place the shortbread cookies in a food processor and grind until they turn into fine crumbs.
Combine the crumbs with the sugar and melted butter in a medium size bowl; mix until coated. Press flat into the bottom of a 9" springform pan and slightly up the edges about 1 inch. Chill the crust in the freezer for about 10 minutes.
Clean out the food processor and add the 1 cup of strawberries and 1/4 cup of sugar. Let sit for a couple minutes so the strawberries can release their juices. Puree the strawberries, set aside.
Meanwhile, make the filling: Using an electric mixer set at medium-high speed, beat the cream cheese and Greek Yogurt until smooth. Gradually beat in the condensed milk, scraping the sides of the bowl as necessary. Beat in the lime juice and strawberry puree until evenly combined.
Pour the mixture into the prepared crust and place back in the freezer for at least 3 hours, or until the center is set.
For the whip cream topping:
In the bowl of your stand mixer, fitted with the whisk attachment, beat the heavy cream until soft peaks start to form. Add the powdered sugar according to your preference of how sweet you want it, and beat until stiff peaks form.
Top the frozen cheesecake with the whip cream and freshly diced strawberries.