Line 10 ramekins with plastic wrap and place them onto a baking sheet.

Hull strawberries with the tip of a knife. Place strawberries in a food processor. Add sugar, Greek yogurt, lemon zest, lemon juice, vanilla extract, and balsamic vinegar. Sprinkle in a tiny pinch of salt. Pulse on and off to combine; finish pureeing on high until smooth.

Whisk heavy cream in a bowl until soft peaks form. Add the strawberry puree. Stir and fold with a spatula until most of the major streaks disappear. Fill ramekins 1/4 to 1/8 inch from the top with the strawberry mixture. Tap baking sheet against the counter to settle the tops. Cover ramekins in plastic wrap and freeze until mostly firm, about 1 1/2 hours.

Meanwhile, place cookies in a resealable plastic bag. Seal; crush cookies through with a rolling pin to get 1 1/2 cups of crumbs. Place crumbs into a bowl; add butter and mix well.

Divide the cookie crumb mixture among the ramekins and smooth out with the back of a spoon. Cover again and freeze until completely frozen, about 2 hours.

Toss diced strawberries with sugar in a bowl. Let rest at room temperature until a syrup forms below the strawberries, about 1 hour.

Warm up each ramekin in your hands to help unmold the semifreddo; invert onto a plate. Top with the strawberries in syrup. Thaw for 10 to 15 minutes before serving.