Position racks in the upper and bottom thirds of the oven. Preheat the oven to 350°F. In a medium bowl, stir together the cookie crumbs and melted butter. Press into the bottom and up the sides of a 9-inch pie plate. On a parchment-lined baking sheet, toss the strawberries with 2 tablespoons of sugar. Transfer both the the oven. Bake the crust until fragrant and slightly dry, about 10 minutes. Leave the strawberries in the oven until they are dark red, very fragrant, and have released most of their juices, about 25 minutes. Cool the crust and the strawberries completely. Transfer half of the strawberries to a food processor or blender and blend until smooth.

In a large bowl, whip 1 cup of heavy cream with the remaining 5 tablespoons of sugar until it holds soft peaks. Blend in the yogurt and vanilla. With a spatula, fold in the strawberry puree just until combined, being careful not to deflate the whipped cream. Pour the filling into the cookie crust. Transfer the pie to the freezer for 1 hour, until the top is set. Wrap with plastic wrap and freeze until completely firm, about 3 hours more. Let the pie soften slightly for 10-15 minutes before slicing and serving. Serve with the remaining roasted strawberries and more whipped cream, if desired.