In a food processor, pulse flour, 2 tablespoons sugar, and cornstarch until combined. Add butter and 1/2 teaspoon vanilla and pulse until fine crumbs form and dough just begins to come together. Press evenly into bottom and up sides of a 9-inch round tart pan with a removable rim.
Bake until edges are golden, about 20 to 22 minutes. Let cool on a rack, then remove tart crust from pan and transfer to a serving plate.
In a bowl with a mixer on high speed, beat the cream until soft peaks form. Add the remaining 2 tablespoons sugar and remaining 1/2 teaspoon vanilla, and beat until thick.
Gently fold the sour cream in the mixture and spread in cooled crust. Arrange strawberries in circles on top. (If you want to create the same effect I did in the photo above, you can alternate the cut sides down and up.)
Cover and chill the tart for 3 to 4 hours to firm up the filling. Cut in slices and serve. Makes 8 servings.
Notes
To store the pie, cover tightly and refrigerate for up to 2 days.